Details
AUTHOR
James Foster \(2025~06~05\)
MODIFIED
James Foster \(2025~06~28\)
DESCRIPTION
Loads the reorganised data from
colour_dance_reorg.csv, saved fromGUV_organisedata.R, and generates plots to show the how dances changed as a function of light stimulus.
INPUTS
colour_dance_reorg.csv,Edrich1979_brightness-accuracy.csv
OUTPUTS
Plotted results.
CHANGES
REFERENCES
Edrich, W., Neumeyer, C. and von Helversen, O. (1979). “Anti-sun orientation” of bees with regard to a field of ultraviolet light. J. Comp. Physiol. 134, 151–157.
Rossel, S. and Wehner, R. (1984). Celestial orientation in bees: the use of spectral cues. J. Comp. Physiol. A 155, 605–613.
TODO
- move necessary functions to GUV_functions
Setting up
First load the functions and packages required for this project.
These can all be found in GUV_functions.R, within the same
Github repository.
Then load the data that will be used. This includes our own dance
data, reorganised by GUV_organisedata.R as
colour_dance_reorg.csv, as well as data from Edrich et
al. (1979) on the relationship between accuracy (mean vector
length), wavelength and intensity. This was manually extracted from Fig.
2 and saved in "Edrich1979_brightness-accuracy.csv.
#Dance angle data
cd = read.table(file = '1Data/colour_dance_reorg.csv',
header = T,
sep = ',')
#Accuracy data
ed = read.table(file = '1Data/Edrich1979_brightness-accuracy.csv',
header = T,
sep = ',')
#Inspect each dataset
print(cd)## bearing run date angle ID brightn colour
## 1 270 1 2016.05.31 -1.57079633 2016.05.31.14.24 l u
## 2 5 2 2016.05.31 0.08726646 2016.05.31.14.24 l u
## 3 20 3 2016.05.31 0.34906585 2016.05.31.14.24 l u
## 4 320 4 2016.05.31 -0.69813170 2016.05.31.14.24 l u
## 5 20 5 2016.05.31 0.34906585 2016.05.31.14.24 l u
## 6 35 6 2016.05.31 0.61086524 2016.05.31.14.24 l u
## 7 10 7 2016.05.31 0.17453293 2016.05.31.14.24 l u
## 8 345 8 2016.05.31 -0.26179939 2016.05.31.14.24 h u
## 9 340 9 2016.05.31 -0.34906585 2016.05.31.14.24 h u
## 10 340 10 2016.05.31 -0.34906585 2016.05.31.14.24 h u
## 11 340 11 2016.05.31 -0.34906585 2016.05.31.14.24 h u
## 12 330 12 2016.05.31 -0.52359878 2016.05.31.14.24 h u
## 13 350 13 2016.05.31 -0.17453293 2016.05.31.14.24 h u
## 14 325 14 2016.05.31 -0.61086524 2016.05.31.14.24 h u
## 15 335 15 2016.05.31 -0.43633231 2016.05.31.14.24 h u
## 16 330 16 2016.05.31 -0.52359878 2016.05.31.14.24 h u
## 17 320 17 2016.05.31 -0.69813170 2016.05.31.14.24 h u
## 18 325 18 2016.05.31 -0.61086524 2016.05.31.14.24 h u
## 19 325 19 2016.05.31 -0.61086524 2016.05.31.14.24 h u
## 20 355 20 2016.05.31 -0.08726646 2016.05.31.14.24 h u
## 21 340 21 2016.05.31 -0.34906585 2016.05.31.14.24 h u
## 22 345 22 2016.05.31 -0.26179939 2016.05.31.14.24 h g
## 23 345 23 2016.05.31 -0.26179939 2016.05.31.14.24 h g
## 24 325 24 2016.05.31 -0.61086524 2016.05.31.14.24 h g
## 25 350 25 2016.05.31 -0.17453293 2016.05.31.14.24 h g
## 26 345 26 2016.05.31 -0.26179939 2016.05.31.14.24 h g
## 27 355 27 2016.05.31 -0.08726646 2016.05.31.14.24 h g
## 28 235 1 2016.05.31 -2.18166156 2016.05.31.14.53 l u
## 29 185 2 2016.05.31 -3.05432619 2016.05.31.14.53 l u
## 30 100 3 2016.05.31 1.74532925 2016.05.31.14.53 l u
## 31 140 4 2016.05.31 2.44346095 2016.05.31.14.53 l u
## 32 90 5 2016.05.31 1.57079633 2016.05.31.14.53 l u
## 33 190 6 2016.05.31 -2.96705973 2016.05.31.14.53 l u
## 34 175 7 2016.05.31 3.05432619 2016.05.31.14.53 l u
## 35 250 8 2016.05.31 -1.91986218 2016.05.31.14.53 l u
## 36 130 9 2016.05.31 2.26892803 2016.05.31.14.53 l u
## 37 160 10 2016.05.31 2.79252680 2016.05.31.14.53 l u
## 38 15 11 2016.05.31 0.26179939 2016.05.31.14.53 h u
## 39 45 12 2016.05.31 0.78539816 2016.05.31.14.53 h u
## 40 15 13 2016.05.31 0.26179939 2016.05.31.14.53 h u
## 41 20 14 2016.05.31 0.34906585 2016.05.31.14.53 h u
## 42 40 15 2016.05.31 0.69813170 2016.05.31.14.53 h u
## 43 20 16 2016.05.31 0.34906585 2016.05.31.14.53 h u
## 44 10 17 2016.05.31 0.17453293 2016.05.31.14.53 h u
## 45 50 18 2016.05.31 0.87266463 2016.05.31.14.53 h u
## 46 10 19 2016.05.31 0.17453293 2016.05.31.14.53 h u
## 47 40 20 2016.05.31 0.69813170 2016.05.31.14.53 h u
## 48 40 21 2016.05.31 0.69813170 2016.05.31.14.53 h u
## 49 50 22 2016.05.31 0.87266463 2016.05.31.14.53 h u
## 50 50 23 2016.05.31 0.87266463 2016.05.31.14.53 h u
## 51 10 24 2016.05.31 0.17453293 2016.05.31.14.53 l g
## 52 40 25 2016.05.31 0.69813170 2016.05.31.14.53 l g
## 53 35 26 2016.05.31 0.61086524 2016.05.31.14.53 l g
## 54 20 27 2016.05.31 0.34906585 2016.05.31.14.53 l g
## 55 30 28 2016.05.31 0.52359878 2016.05.31.14.53 l g
## 56 40 29 2016.05.31 0.69813170 2016.05.31.14.53 l g
## 57 20 30 2016.05.31 0.34906585 2016.05.31.14.53 l g
## 58 25 31 2016.05.31 0.43633231 2016.05.31.14.53 l g
## 59 20 32 2016.05.31 0.34906585 2016.05.31.14.53 l g
## 60 40 33 2016.05.31 0.69813170 2016.05.31.14.53 l g
## 61 20 34 2016.05.31 0.34906585 2016.05.31.14.53 h g
## 62 20 35 2016.05.31 0.34906585 2016.05.31.14.53 h g
## 63 200 1 2016.05.31 -2.79252680 2016.05.31.14.57 l u
## 64 140 2 2016.05.31 2.44346095 2016.05.31.14.57 l u
## 65 220 3 2016.05.31 -2.44346095 2016.05.31.14.57 l u
## 66 150 4 2016.05.31 2.61799388 2016.05.31.14.57 l u
## 67 170 5 2016.05.31 2.96705973 2016.05.31.14.57 l u
## 68 100 6 2016.05.31 1.74532925 2016.05.31.14.57 l u
## 69 155 7 2016.05.31 2.70526034 2016.05.31.14.57 l u
## 70 90 8 2016.05.31 1.57079633 2016.05.31.14.57 l u
## 71 155 9 2016.05.31 2.70526034 2016.05.31.14.57 l u
## 72 355 10 2016.05.31 -0.08726646 2016.05.31.14.57 h u
## 73 40 11 2016.05.31 0.69813170 2016.05.31.14.57 h u
## 74 70 12 2016.05.31 1.22173048 2016.05.31.14.57 h u
## 75 30 13 2016.05.31 0.52359878 2016.05.31.14.57 h u
## 76 70 14 2016.05.31 1.22173048 2016.05.31.14.57 h u
## 77 25 15 2016.05.31 0.43633231 2016.05.31.14.57 h u
## 78 20 16 2016.05.31 0.34906585 2016.05.31.14.57 h u
## 79 30 17 2016.05.31 0.52359878 2016.05.31.14.57 h u
## 80 30 18 2016.05.31 0.52359878 2016.05.31.14.57 h u
## 81 70 19 2016.05.31 1.22173048 2016.05.31.14.57 h u
## 82 60 20 2016.05.31 1.04719755 2016.05.31.14.57 h u
## 83 40 21 2016.05.31 0.69813170 2016.05.31.14.57 h u
## 84 60 22 2016.05.31 1.04719755 2016.05.31.14.57 h u
## 85 40 23 2016.05.31 0.69813170 2016.05.31.14.57 h u
## 86 100 1 2016.05.31 1.74532925 2016.05.31.15.14 l u
## 87 110 2 2016.05.31 1.91986218 2016.05.31.15.14 l u
## 88 140 3 2016.05.31 2.44346095 2016.05.31.15.14 l u
## 89 110 4 2016.05.31 1.91986218 2016.05.31.15.14 l u
## 90 140 5 2016.05.31 2.44346095 2016.05.31.15.14 l u
## 91 130 6 2016.05.31 2.26892803 2016.05.31.15.14 l u
## 92 110 7 2016.05.31 1.91986218 2016.05.31.15.14 l u
## 93 95 8 2016.05.31 1.65806279 2016.05.31.15.14 l u
## 94 140 9 2016.05.31 2.44346095 2016.05.31.15.14 l u
## 95 80 10 2016.05.31 1.39626340 2016.05.31.15.14 l u
## 96 120 11 2016.05.31 2.09439510 2016.05.31.15.14 l u
## 97 60 12 2016.05.31 1.04719755 2016.05.31.15.14 h u
## 98 60 13 2016.05.31 1.04719755 2016.05.31.15.14 h u
## 99 50 14 2016.05.31 0.87266463 2016.05.31.15.14 h u
## 100 85 15 2016.05.31 1.48352986 2016.05.31.15.14 h u
## 101 40 16 2016.05.31 0.69813170 2016.05.31.15.14 h u
## 102 40 17 2016.05.31 0.69813170 2016.05.31.15.14 h u
## 103 20 18 2016.05.31 0.34906585 2016.05.31.15.14 h u
## 104 270 1 2016.05.31 -1.57079633 2016.05.31.14.18 l u
## 105 260 2 2016.05.31 -1.74532925 2016.05.31.14.18 l u
## 106 310 3 2016.05.31 -0.87266463 2016.05.31.14.18 l u
## 107 305 4 2016.05.31 -0.95993109 2016.05.31.14.18 l u
## 108 10 5 2016.05.31 0.17453293 2016.05.31.14.18 l u
## 109 350 6 2016.05.31 -0.17453293 2016.05.31.14.18 l u
## 110 270 7 2016.05.31 -1.57079633 2016.05.31.14.18 l u
## 111 310 8 2016.05.31 -0.87266463 2016.05.31.14.18 l u
## 112 60 9 2016.05.31 1.04719755 2016.05.31.14.18 h u
## 113 10 10 2016.05.31 0.17453293 2016.05.31.14.18 h u
## 114 5 11 2016.05.31 0.08726646 2016.05.31.14.18 h u
## 115 40 12 2016.05.31 0.69813170 2016.05.31.14.18 h u
## 116 10 13 2016.05.31 0.17453293 2016.05.31.14.18 h u
## 117 5 14 2016.05.31 0.08726646 2016.05.31.14.18 h u
## 118 10 15 2016.05.31 0.17453293 2016.05.31.14.18 h u
## 119 10 16 2016.05.31 0.17453293 2016.05.31.14.18 h u
## 120 30 17 2016.05.31 0.52359878 2016.05.31.14.18 h u
## 121 0 18 2016.05.31 0.00000000 2016.05.31.14.18 h u
## 122 15 19 2016.05.31 0.26179939 2016.05.31.14.18 h u
## 123 15 20 2016.05.31 0.26179939 2016.05.31.14.18 h u
## 124 15 21 2016.05.31 0.26179939 2016.05.31.14.18 h u
## 125 15 22 2016.05.31 0.26179939 2016.05.31.14.18 h u
## 126 5 23 2016.05.31 0.08726646 2016.05.31.14.18 l g
## 127 5 24 2016.05.31 0.08726646 2016.05.31.14.18 l g
## 128 40 25 2016.05.31 0.69813170 2016.05.31.14.18 l g
## 129 20 26 2016.05.31 0.34906585 2016.05.31.14.18 l g
## 130 30 27 2016.05.31 0.52359878 2016.05.31.14.18 l g
## 131 20 28 2016.05.31 0.34906585 2016.05.31.14.18 l g
## 132 60 29 2016.05.31 1.04719755 2016.05.31.14.18 l g
## 133 50 30 2016.05.31 0.87266463 2016.05.31.14.18 l g
## 134 60 31 2016.05.31 1.04719755 2016.05.31.14.18 l g
## 135 60 32 2016.05.31 1.04719755 2016.05.31.14.18 l g
## 136 5 33 2016.05.31 0.08726646 2016.05.31.14.18 h g
## 137 45 34 2016.05.31 0.78539816 2016.05.31.14.18 h g
## 138 40 35 2016.05.31 0.69813170 2016.05.31.14.18 h g
## 139 40 36 2016.05.31 0.69813170 2016.05.31.14.18 h g
## 140 30 37 2016.05.31 0.52359878 2016.05.31.14.18 h g
## 141 200 1 2016.05.31 -2.79252680 2016.05.31.14.02 l u
## 142 310 2 2016.05.31 -0.87266463 2016.05.31.14.02 l u
## 143 230 3 2016.05.31 -2.26892803 2016.05.31.14.02 l u
## 144 240 4 2016.05.31 -2.09439510 2016.05.31.14.02 l u
## 145 230 5 2016.05.31 -2.26892803 2016.05.31.14.02 l u
## 146 225 6 2016.05.31 -2.35619449 2016.05.31.14.02 l u
## 147 130 7 2016.05.31 2.26892803 2016.05.31.14.02 l u
## 148 150 8 2016.05.31 2.61799388 2016.05.31.14.02 l u
## 149 240 9 2016.05.31 -2.09439510 2016.05.31.14.02 l u
## 150 265 10 2016.05.31 -1.65806279 2016.05.31.14.02 h u
## 151 300 11 2016.05.31 -1.04719755 2016.05.31.14.02 h u
## 152 260 12 2016.05.31 -1.74532925 2016.05.31.14.02 h u
## 153 255 13 2016.05.31 -1.83259571 2016.05.31.14.02 h u
## 154 270 14 2016.05.31 -1.57079633 2016.05.31.14.02 h u
## 155 240 15 2016.05.31 -2.09439510 2016.05.31.14.02 h u
## 156 280 16 2016.05.31 -1.39626340 2016.05.31.14.02 h u
## 157 250 17 2016.05.31 -1.91986218 2016.05.31.14.02 h u
## 158 310 18 2016.05.31 -0.87266463 2016.05.31.14.02 h u
## 159 260 19 2016.05.31 -1.74532925 2016.05.31.14.02 h u
## 160 310 20 2016.05.31 -0.87266463 2016.05.31.14.02 h u
## 161 305 1 2016.06.06 -0.95993109 2016.06.06.14.10 l u
## 162 115 2 2016.06.06 2.00712864 2016.06.06.14.10 l u
## 163 310 3 2016.06.06 -0.87266463 2016.06.06.14.10 l u
## 164 20 4 2016.06.06 0.34906585 2016.06.06.14.10 l u
## 165 140 5 2016.06.06 2.44346095 2016.06.06.14.10 l u
## 166 0 6 2016.06.06 0.00000000 2016.06.06.14.10 l u
## 167 140 7 2016.06.06 2.44346095 2016.06.06.14.10 l u
## 168 15 8 2016.06.06 0.26179939 2016.06.06.14.10 l u
## 169 40 9 2016.06.06 0.69813170 2016.06.06.14.10 l u
## 170 5 10 2016.06.06 0.08726646 2016.06.06.14.10 l u
## 171 30 11 2016.06.06 0.52359878 2016.06.06.14.10 l u
## 172 55 12 2016.06.06 0.95993109 2016.06.06.14.10 l u
## 173 330 13 2016.06.06 -0.52359878 2016.06.06.14.10 h u
## 174 350 14 2016.06.06 -0.17453293 2016.06.06.14.10 h u
## 175 30 15 2016.06.06 0.52359878 2016.06.06.14.10 h u
## 176 350 16 2016.06.06 -0.17453293 2016.06.06.14.10 h u
## 177 335 17 2016.06.06 -0.43633231 2016.06.06.14.10 h u
## 178 0 18 2016.06.06 0.00000000 2016.06.06.14.10 h u
## 179 340 19 2016.06.06 -0.34906585 2016.06.06.14.10 h u
## 180 355 20 2016.06.06 -0.08726646 2016.06.06.14.10 h u
## 181 10 21 2016.06.06 0.17453293 2016.06.06.14.10 h u
## 182 335 22 2016.06.06 -0.43633231 2016.06.06.14.10 h u
## 183 5 23 2016.06.06 0.08726646 2016.06.06.14.10 h u
## 184 355 24 2016.06.06 -0.08726646 2016.06.06.14.10 h u
## 185 295 25 2016.06.06 -1.13446401 2016.06.06.14.10 h u
## 186 330 26 2016.06.06 -0.52359878 2016.06.06.14.10 h u
## 187 0 27 2016.06.06 0.00000000 2016.06.06.14.10 l g
## 188 30 28 2016.06.06 0.52359878 2016.06.06.14.10 l g
## 189 25 29 2016.06.06 0.43633231 2016.06.06.14.10 l g
## 190 55 30 2016.06.06 0.95993109 2016.06.06.14.10 l g
## 191 35 31 2016.06.06 0.61086524 2016.06.06.14.10 l g
## 192 10 32 2016.06.06 0.17453293 2016.06.06.14.10 l g
## 193 5 33 2016.06.06 0.08726646 2016.06.06.14.10 l g
## 194 15 34 2016.06.06 0.26179939 2016.06.06.14.10 l g
## 195 20 35 2016.06.06 0.34906585 2016.06.06.14.10 l g
## 196 20 36 2016.06.06 0.34906585 2016.06.06.14.10 l g
## 197 20 37 2016.06.06 0.34906585 2016.06.06.14.10 l g
## 198 120 38 2016.06.06 2.09439510 2016.06.06.14.10 l g
## 199 330 39 2016.06.06 -0.52359878 2016.06.06.14.10 l g
## 200 355 40 2016.06.06 -0.08726646 2016.06.06.14.10 l g
## 201 155 1 2016.06.06 2.70526034 2016.06.06.14.16 l u
## 202 180 2 2016.06.06 3.14159265 2016.06.06.14.16 l u
## 203 165 3 2016.06.06 2.87979327 2016.06.06.14.16 l u
## 204 185 4 2016.06.06 -3.05432619 2016.06.06.14.16 l u
## 205 190 5 2016.06.06 -2.96705973 2016.06.06.14.16 l u
## 206 225 6 2016.06.06 -2.35619449 2016.06.06.14.16 l u
## 207 195 7 2016.06.06 -2.87979327 2016.06.06.14.16 l u
## 208 220 8 2016.06.06 -2.44346095 2016.06.06.14.16 l u
## 209 180 9 2016.06.06 3.14159265 2016.06.06.14.16 l u
## 210 190 10 2016.06.06 -2.96705973 2016.06.06.14.16 l u
## 211 205 11 2016.06.06 -2.70526034 2016.06.06.14.16 l u
## 212 240 12 2016.06.06 -2.09439510 2016.06.06.14.16 l u
## 213 180 13 2016.06.06 3.14159265 2016.06.06.14.16 l u
## 214 230 14 2016.06.06 -2.26892803 2016.06.06.14.16 l u
## 215 140 15 2016.06.06 2.44346095 2016.06.06.14.16 h u
## 216 140 16 2016.06.06 2.44346095 2016.06.06.14.16 h u
## 217 150 17 2016.06.06 2.61799388 2016.06.06.14.16 h u
## 218 140 18 2016.06.06 2.44346095 2016.06.06.14.16 h u
## 219 120 1 2016.06.06 2.09439510 2016.06.06.14.22 l u
## 220 145 2 2016.06.06 2.53072742 2016.06.06.14.22 l u
## 221 320 3 2016.06.06 -0.69813170 2016.06.06.14.22 l u
## 222 170 4 2016.06.06 2.96705973 2016.06.06.14.22 l u
## 223 160 5 2016.06.06 2.79252680 2016.06.06.14.22 l u
## 224 170 6 2016.06.06 2.96705973 2016.06.06.14.22 l u
## 225 155 7 2016.06.06 2.70526034 2016.06.06.14.22 l u
## 226 190 8 2016.06.06 -2.96705973 2016.06.06.14.22 l u
## 227 185 9 2016.06.06 -3.05432619 2016.06.06.14.22 l u
## 228 185 10 2016.06.06 -3.05432619 2016.06.06.14.22 l u
## 229 150 11 2016.06.06 2.61799388 2016.06.06.14.22 l u
## 230 165 12 2016.06.06 2.87979327 2016.06.06.14.22 l u
## 231 155 13 2016.06.06 2.70526034 2016.06.06.14.22 l u
## 232 180 14 2016.06.06 3.14159265 2016.06.06.14.22 l u
## 233 175 15 2016.06.06 3.05432619 2016.06.06.14.22 l u
## 234 190 16 2016.06.06 -2.96705973 2016.06.06.14.22 l u
## 235 165 17 2016.06.06 2.87979327 2016.06.06.14.22 l u
## 236 155 18 2016.06.06 2.70526034 2016.06.06.14.22 l u
## 237 160 19 2016.06.06 2.79252680 2016.06.06.14.22 l u
## 238 35 20 2016.06.06 0.61086524 2016.06.06.14.22 h u
## 239 30 21 2016.06.06 0.52359878 2016.06.06.14.22 h u
## 240 45 22 2016.06.06 0.78539816 2016.06.06.14.22 h u
## 241 40 23 2016.06.06 0.69813170 2016.06.06.14.22 h u
## 242 80 24 2016.06.06 1.39626340 2016.06.06.14.22 h u
## 243 35 25 2016.06.06 0.61086524 2016.06.06.14.22 h u
## 244 60 26 2016.06.06 1.04719755 2016.06.06.14.22 h u
## 245 30 27 2016.06.06 0.52359878 2016.06.06.14.22 h u
## 246 40 28 2016.06.06 0.69813170 2016.06.06.14.22 h u
## 247 50 29 2016.06.06 0.87266463 2016.06.06.14.22 h u
## 248 10 30 2016.06.06 0.17453293 2016.06.06.14.22 h u
## 249 50 31 2016.06.06 0.87266463 2016.06.06.14.22 h u
## 250 65 32 2016.06.06 1.13446401 2016.06.06.14.22 h u
## 251 90 33 2016.06.06 1.57079633 2016.06.06.14.22 h u
## 252 85 34 2016.06.06 1.48352986 2016.06.06.14.22 h u
## 253 35 35 2016.06.06 0.61086524 2016.06.06.14.22 h u
## 254 55 36 2016.06.06 0.95993109 2016.06.06.14.22 h u
## 255 40 37 2016.06.06 0.69813170 2016.06.06.14.22 h u
## 256 110 38 2016.06.06 1.91986218 2016.06.06.14.22 h u
## 257 165 39 2016.06.06 2.87979327 2016.06.06.14.22 l g
## 258 120 40 2016.06.06 2.09439510 2016.06.06.14.22 l g
## 259 120 41 2016.06.06 2.09439510 2016.06.06.14.22 l g
## 260 170 42 2016.06.06 2.96705973 2016.06.06.14.22 l g
## 261 90 43 2016.06.06 1.57079633 2016.06.06.14.22 l g
## 262 150 44 2016.06.06 2.61799388 2016.06.06.14.22 l g
## 263 160 45 2016.06.06 2.79252680 2016.06.06.14.22 l g
## 264 175 46 2016.06.06 3.05432619 2016.06.06.14.22 l g
## 265 40 47 2016.06.06 0.69813170 2016.06.06.14.22 l g
## 266 160 48 2016.06.06 2.79252680 2016.06.06.14.22 l g
## 267 155 49 2016.06.06 2.70526034 2016.06.06.14.22 l g
## 268 120 50 2016.06.06 2.09439510 2016.06.06.14.22 l g
## 269 110 51 2016.06.06 1.91986218 2016.06.06.14.22 l g
## 270 200 52 2016.06.06 -2.79252680 2016.06.06.14.22 l g
## 271 140 53 2016.06.06 2.44346095 2016.06.06.14.22 l g
## 272 140 54 2016.06.06 2.44346095 2016.06.06.14.22 l g
## 273 130 55 2016.06.06 2.26892803 2016.06.06.14.22 l g
## 274 60 56 2016.06.06 1.04719755 2016.06.06.14.22 l g
## 275 40 57 2016.06.06 0.69813170 2016.06.06.14.22 h g
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## 1883 15 40 2016.07.18 0.26179939 2016.07.18.15.18 h g
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## 1885 15 42 2016.07.18 0.26179939 2016.07.18.15.18 h g
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## 1901 90 16 2016.07.18 1.57079633 2016.07.18.15.28 l u
## 1902 110 17 2016.07.18 1.91986218 2016.07.18.15.28 l u
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## 1906 160 21 2016.07.18 2.79252680 2016.07.18.15.28 l u
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## 1908 45 23 2016.07.18 0.78539816 2016.07.18.15.28 h u
## 1909 45 24 2016.07.18 0.78539816 2016.07.18.15.28 h u
## 1910 355 25 2016.07.18 -0.08726646 2016.07.18.15.28 h u
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## 1912 15 27 2016.07.18 0.26179939 2016.07.18.15.28 h u
## 1913 45 28 2016.07.18 0.78539816 2016.07.18.15.28 h u
## 1914 55 29 2016.07.18 0.95993109 2016.07.18.15.28 h u
## 1915 60 30 2016.07.18 1.04719755 2016.07.18.15.28 h u
## 1916 20 31 2016.07.18 0.34906585 2016.07.18.15.28 h u
## 1917 30 32 2016.07.18 0.52359878 2016.07.18.15.28 h u
## 1918 20 33 2016.07.18 0.34906585 2016.07.18.15.28 h u
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## 1920 355 2 2016.07.19 -0.08726646 2016.07.19.12.15 l u
## 1921 210 3 2016.07.19 -2.61799388 2016.07.19.12.15 l u
## 1922 220 4 2016.07.19 -2.44346095 2016.07.19.12.15 l u
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## 1926 210 8 2016.07.19 -2.61799388 2016.07.19.12.15 l u
## 1927 250 9 2016.07.19 -1.91986218 2016.07.19.12.15 l u
## 1928 320 10 2016.07.19 -0.69813170 2016.07.19.12.15 l u
## 1929 20 11 2016.07.19 0.34906585 2016.07.19.12.15 l u
## 1930 30 12 2016.07.19 0.52359878 2016.07.19.12.15 l u
## 1931 280 13 2016.07.19 -1.39626340 2016.07.19.12.15 l u
## 1932 245 14 2016.07.19 -2.00712864 2016.07.19.12.15 l u
## 1933 285 15 2016.07.19 -1.30899694 2016.07.19.12.15 l u
## 1934 270 16 2016.07.19 -1.57079633 2016.07.19.12.15 l u
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## 1936 310 18 2016.07.19 -0.87266463 2016.07.19.12.15 h u
## 1937 305 19 2016.07.19 -0.95993109 2016.07.19.12.15 h u
## 1938 320 20 2016.07.19 -0.69813170 2016.07.19.12.15 h u
## 1939 270 21 2016.07.19 -1.57079633 2016.07.19.12.15 h u
## 1940 310 22 2016.07.19 -0.87266463 2016.07.19.12.15 h u
## 1941 325 23 2016.07.19 -0.61086524 2016.07.19.12.15 h u
## 1942 340 24 2016.07.19 -0.34906585 2016.07.19.12.15 h u
## 1943 0 25 2016.07.19 0.00000000 2016.07.19.12.15 h u
## 1944 345 26 2016.07.19 -0.26179939 2016.07.19.12.15 h u
## 1945 340 27 2016.07.19 -0.34906585 2016.07.19.12.15 h u
## 1946 300 28 2016.07.19 -1.04719755 2016.07.19.12.15 h u
## 1947 350 29 2016.07.19 -0.17453293 2016.07.19.12.15 h u
## 1948 340 30 2016.07.19 -0.34906585 2016.07.19.12.15 h u
## 1949 345 31 2016.07.19 -0.26179939 2016.07.19.12.15 h u
## 1950 350 32 2016.07.19 -0.17453293 2016.07.19.12.15 h u
## 1951 350 33 2016.07.19 -0.17453293 2016.07.19.12.15 h g
## 1952 345 34 2016.07.19 -0.26179939 2016.07.19.12.15 h g
## 1953 350 35 2016.07.19 -0.17453293 2016.07.19.12.15 h g
## 1954 315 36 2016.07.19 -0.78539816 2016.07.19.12.15 h g
## 1955 340 37 2016.07.19 -0.34906585 2016.07.19.12.15 h g
## 1956 345 38 2016.07.19 -0.26179939 2016.07.19.12.15 h g
## 1957 340 39 2016.07.19 -0.34906585 2016.07.19.12.15 h g
## 1958 310 40 2016.07.19 -0.87266463 2016.07.19.12.15 h g
## 1959 50 1 2016.07.19 0.87266463 2016.07.19.12.59 l u
## 1960 80 2 2016.07.19 1.39626340 2016.07.19.12.59 l u
## 1961 100 3 2016.07.19 1.74532925 2016.07.19.12.59 l u
## 1962 60 4 2016.07.19 1.04719755 2016.07.19.12.59 l u
## 1963 200 5 2016.07.19 -2.79252680 2016.07.19.12.59 l u
## 1964 330 6 2016.07.19 -0.52359878 2016.07.19.12.59 l u
## 1965 80 7 2016.07.19 1.39626340 2016.07.19.12.59 l u
## 1966 90 8 2016.07.19 1.57079633 2016.07.19.12.59 l u
## 1967 110 9 2016.07.19 1.91986218 2016.07.19.12.59 l u
## 1968 30 10 2016.07.19 0.52359878 2016.07.19.12.59 l u
## 1969 90 11 2016.07.19 1.57079633 2016.07.19.12.59 l u
## 1970 35 12 2016.07.19 0.61086524 2016.07.19.12.59 l u
## 1971 95 13 2016.07.19 1.65806279 2016.07.19.12.59 l u
## 1972 70 14 2016.07.19 1.22173048 2016.07.19.12.59 l u
## 1973 80 15 2016.07.19 1.39626340 2016.07.19.12.59 l u
## 1974 10 16 2016.07.19 0.17453293 2016.07.19.12.59 l u
## 1975 70 17 2016.07.19 1.22173048 2016.07.19.12.59 l u
## 1976 60 18 2016.07.19 1.04719755 2016.07.19.12.59 h u
## 1977 0 19 2016.07.19 0.00000000 2016.07.19.12.59 h u
## 1978 35 20 2016.07.19 0.61086524 2016.07.19.12.59 h u
## 1979 20 21 2016.07.19 0.34906585 2016.07.19.12.59 h u
## 1980 20 22 2016.07.19 0.34906585 2016.07.19.12.59 h u
## 1981 25 23 2016.07.19 0.43633231 2016.07.19.12.59 h u
## 1982 25 24 2016.07.19 0.43633231 2016.07.19.12.59 h u
## 1983 70 25 2016.07.19 1.22173048 2016.07.19.12.59 h u
## 1984 20 26 2016.07.19 0.34906585 2016.07.19.12.59 h u
## 1985 50 27 2016.07.19 0.87266463 2016.07.19.12.59 h u
## 1986 30 28 2016.07.19 0.52359878 2016.07.19.12.59 h u
## 1987 60 29 2016.07.19 1.04719755 2016.07.19.12.59 h u
## 1988 30 30 2016.07.19 0.52359878 2016.07.19.12.59 h u
## 1989 40 31 2016.07.19 0.69813170 2016.07.19.12.59 h u
## 1990 60 32 2016.07.19 1.04719755 2016.07.19.12.59 h u
## 1991 20 33 2016.07.19 0.34906585 2016.07.19.12.59 h u
## 1992 50 34 2016.07.19 0.87266463 2016.07.19.12.59 h u
## 1993 40 35 2016.07.19 0.69813170 2016.07.19.12.59 h u
## 1994 40 36 2016.07.19 0.69813170 2016.07.19.12.59 h u
## 1995 160 1 2016.07.19 2.79252680 2016.07.19.13.04 l u
## 1996 150 2 2016.07.19 2.61799388 2016.07.19.13.04 l u
## 1997 200 3 2016.07.19 -2.79252680 2016.07.19.13.04 l u
## 1998 25 4 2016.07.19 0.43633231 2016.07.19.13.04 l u
## 1999 100 5 2016.07.19 1.74532925 2016.07.19.13.04 l u
## 2000 200 6 2016.07.19 -2.79252680 2016.07.19.13.04 l u
## 2001 340 7 2016.07.19 -0.34906585 2016.07.19.13.04 l u
## 2002 15 8 2016.07.19 0.26179939 2016.07.19.13.04 l u
## 2003 300 9 2016.07.19 -1.04719755 2016.07.19.13.04 l u
## 2004 330 10 2016.07.19 -0.52359878 2016.07.19.13.04 l u
## 2005 345 11 2016.07.19 -0.26179939 2016.07.19.13.04 l u
## 2006 250 12 2016.07.19 -1.91986218 2016.07.19.13.04 l u
## 2007 340 13 2016.07.19 -0.34906585 2016.07.19.13.04 l u
## 2008 0 14 2016.07.19 0.00000000 2016.07.19.13.04 l u
## 2009 300 15 2016.07.19 -1.04719755 2016.07.19.13.04 l u
## 2010 10 16 2016.07.19 0.17453293 2016.07.19.13.04 l u
## 2011 310 17 2016.07.19 -0.87266463 2016.07.19.13.04 l u
## 2012 310 18 2016.07.19 -0.87266463 2016.07.19.13.04 h u
## 2013 345 19 2016.07.19 -0.26179939 2016.07.19.13.04 h u
## 2014 355 20 2016.07.19 -0.08726646 2016.07.19.13.04 h u
## 2015 305 21 2016.07.19 -0.95993109 2016.07.19.13.04 h u
## 2016 325 22 2016.07.19 -0.61086524 2016.07.19.13.04 h u
## 2017 325 23 2016.07.19 -0.61086524 2016.07.19.13.04 h u
## 2018 350 24 2016.07.19 -0.17453293 2016.07.19.13.04 h u
## 2019 350 25 2016.07.19 -0.17453293 2016.07.19.13.04 h u
## 2020 0 26 2016.07.19 0.00000000 2016.07.19.13.04 h u
## 2021 355 27 2016.07.19 -0.08726646 2016.07.19.13.04 h u
## 2022 350 28 2016.07.19 -0.17453293 2016.07.19.13.04 h u
## 2023 340 29 2016.07.19 -0.34906585 2016.07.19.13.04 h u
## 2024 310 30 2016.07.19 -0.87266463 2016.07.19.13.04 h u
## 2025 345 31 2016.07.19 -0.26179939 2016.07.19.13.04 h u
## 2026 340 32 2016.07.19 -0.34906585 2016.07.19.13.04 h u
## 2027 355 33 2016.07.19 -0.08726646 2016.07.19.13.04 h u
## 2028 340 34 2016.07.19 -0.34906585 2016.07.19.13.04 h u
## 2029 340 35 2016.07.19 -0.34906585 2016.07.19.13.04 h u
## 2030 330 36 2016.07.19 -0.52359878 2016.07.19.13.04 h u
## 2031 330 37 2016.07.19 -0.52359878 2016.07.19.13.04 h u
## 2032 90 1 2016.08.17 1.57079633 2016.08.17.13.46 l u
## 2033 80 2 2016.08.17 1.39626340 2016.08.17.13.46 l u
## 2034 40 3 2016.08.17 0.69813170 2016.08.17.13.46 l u
## 2035 70 4 2016.08.17 1.22173048 2016.08.17.13.46 l u
## 2036 40 5 2016.08.17 0.69813170 2016.08.17.13.46 l u
## 2037 50 6 2016.08.17 0.87266463 2016.08.17.13.46 l u
## 2038 350 7 2016.08.17 -0.17453293 2016.08.17.13.46 l u
## 2039 355 8 2016.08.17 -0.08726646 2016.08.17.13.46 l u
## 2040 70 9 2016.08.17 1.22173048 2016.08.17.13.46 l u
## 2041 90 10 2016.08.17 1.57079633 2016.08.17.13.46 l u
## 2042 70 11 2016.08.17 1.22173048 2016.08.17.13.46 l u
## 2043 75 12 2016.08.17 1.30899694 2016.08.17.13.46 l u
## 2044 345 13 2016.08.17 -0.26179939 2016.08.17.13.46 h u
## 2045 290 14 2016.08.17 -1.22173048 2016.08.17.13.46 h u
## 2046 290 15 2016.08.17 -1.22173048 2016.08.17.13.46 h u
## 2047 295 16 2016.08.17 -1.13446401 2016.08.17.13.46 h u
## 2048 310 17 2016.08.17 -0.87266463 2016.08.17.13.46 h u
## 2049 290 18 2016.08.17 -1.22173048 2016.08.17.13.46 h u
## 2050 290 19 2016.08.17 -1.22173048 2016.08.17.13.46 h u
## 2051 310 20 2016.08.17 -0.87266463 2016.08.17.13.46 h u
## 2052 290 21 2016.08.17 -1.22173048 2016.08.17.13.46 h u
## 2053 280 22 2016.08.17 -1.39626340 2016.08.17.13.46 h u
## 2054 345 23 2016.08.17 -0.26179939 2016.08.17.13.46 h u
## 2055 330 24 2016.08.17 -0.52359878 2016.08.17.13.46 h u
## 2056 295 25 2016.08.17 -1.13446401 2016.08.17.13.46 h u
## 2057 185 1 2016.08.17 -3.05432619 2016.08.17.14.47 l u
## 2058 65 2 2016.08.17 1.13446401 2016.08.17.14.47 l u
## 2059 120 3 2016.08.17 2.09439510 2016.08.17.14.47 l u
## 2060 185 4 2016.08.17 -3.05432619 2016.08.17.14.47 l u
## 2061 200 5 2016.08.17 -2.79252680 2016.08.17.14.47 l u
## 2062 90 6 2016.08.17 1.57079633 2016.08.17.14.47 l u
## 2063 175 7 2016.08.17 3.05432619 2016.08.17.14.47 l u
## 2064 155 8 2016.08.17 2.70526034 2016.08.17.14.47 l u
## 2065 105 9 2016.08.17 1.83259571 2016.08.17.14.47 l u
## 2066 115 10 2016.08.17 2.00712864 2016.08.17.14.47 l u
## 2067 50 11 2016.08.17 0.87266463 2016.08.17.14.47 l u
## 2068 90 12 2016.08.17 1.57079633 2016.08.17.14.47 l u
## 2069 180 13 2016.08.17 3.14159265 2016.08.17.14.47 l u
## 2070 140 14 2016.08.17 2.44346095 2016.08.17.14.47 l u
## 2071 110 15 2016.08.17 1.91986218 2016.08.17.14.47 l u
## 2072 290 25 2016.08.17 -1.22173048 2016.08.17.14.47 h u
## 2073 300 26 2016.08.17 -1.04719755 2016.08.17.14.47 h u
## 2074 330 27 2016.08.17 -0.52359878 2016.08.17.14.47 h u
## 2075 310 28 2016.08.17 -0.87266463 2016.08.17.14.47 h u
## 2076 330 29 2016.08.17 -0.52359878 2016.08.17.14.47 h u
## 2077 320 30 2016.08.17 -0.69813170 2016.08.17.14.47 h u
## 2078 300 31 2016.08.17 -1.04719755 2016.08.17.14.47 h u
## 2079 320 32 2016.08.17 -0.69813170 2016.08.17.14.47 h u
## 2080 330 33 2016.08.17 -0.52359878 2016.08.17.14.47 h u
## 2081 320 34 2016.08.17 -0.69813170 2016.08.17.14.47 h u
## 2082 300 35 2016.08.17 -1.04719755 2016.08.17.14.47 h u
## 2083 310 36 2016.08.17 -0.87266463 2016.08.17.14.47 h u
## 2084 345 37 2016.08.17 -0.26179939 2016.08.17.14.47 h u
## 2085 325 38 2016.08.17 -0.61086524 2016.08.17.14.47 h u
## 2086 310 39 2016.08.17 -0.87266463 2016.08.17.14.47 h u
## 2087 340 40 2016.08.17 -0.34906585 2016.08.17.14.47 h u
## 2088 190 1 2016.08.17 -2.96705973 2016.08.17.16.22 l u
## 2089 280 2 2016.08.17 -1.39626340 2016.08.17.16.22 l u
## 2090 90 3 2016.08.17 1.57079633 2016.08.17.16.22 l u
## 2091 135 4 2016.08.17 2.35619449 2016.08.17.16.22 l u
## 2092 170 5 2016.08.17 2.96705973 2016.08.17.16.22 l u
## 2093 150 6 2016.08.17 2.61799388 2016.08.17.16.22 l u
## 2094 200 7 2016.08.17 -2.79252680 2016.08.17.16.22 l u
## 2095 120 8 2016.08.17 2.09439510 2016.08.17.16.22 l u
## 2096 110 9 2016.08.17 1.91986218 2016.08.17.16.22 l u
## 2097 100 10 2016.08.17 1.74532925 2016.08.17.16.22 l u
## 2098 330 11 2016.08.17 -0.52359878 2016.08.17.16.22 l u
## 2099 100 12 2016.08.17 1.74532925 2016.08.17.16.22 l u
## 2100 50 13 2016.08.17 0.87266463 2016.08.17.16.22 l u
## 2101 120 14 2016.08.17 2.09439510 2016.08.17.16.22 l u
## 2102 10 15 2016.08.17 0.17453293 2016.08.17.16.22 l u
## 2103 160 16 2016.08.17 2.79252680 2016.08.17.16.22 l u
## 2104 150 17 2016.08.17 2.61799388 2016.08.17.16.22 l u
## 2105 110 18 2016.08.17 1.91986218 2016.08.17.16.22 l u
## 2106 190 19 2016.08.17 -2.96705973 2016.08.17.16.22 l u
## 2107 170 20 2016.08.17 2.96705973 2016.08.17.16.22 l u
## 2108 340 21 2016.08.17 -0.34906585 2016.08.17.16.22 h u
## 2109 320 22 2016.08.17 -0.69813170 2016.08.17.16.22 h u
## 2110 320 23 2016.08.17 -0.69813170 2016.08.17.16.22 h u
## 2111 350 24 2016.08.17 -0.17453293 2016.08.17.16.22 h u
## 2112 340 25 2016.08.17 -0.34906585 2016.08.17.16.22 h u
## 2113 330 26 2016.08.17 -0.52359878 2016.08.17.16.22 h u
## 2114 340 27 2016.08.17 -0.34906585 2016.08.17.16.22 h u
## 2115 320 28 2016.08.17 -0.69813170 2016.08.17.16.22 h u
## 2116 310 29 2016.08.17 -0.87266463 2016.08.17.16.22 h u
## 2117 300 30 2016.08.17 -1.04719755 2016.08.17.16.22 h u
## 2118 335 31 2016.08.17 -0.43633231 2016.08.17.16.22 h u
## 2119 320 32 2016.08.17 -0.69813170 2016.08.17.16.22 h u
## 2120 340 1 2016.08.17 -0.34906585 2016.08.17.16.27 l u
## 2121 310 2 2016.08.17 -0.87266463 2016.08.17.16.27 l u
## 2122 110 3 2016.08.17 1.91986218 2016.08.17.16.27 l u
## 2123 160 4 2016.08.17 2.79252680 2016.08.17.16.27 l u
## 2124 350 5 2016.08.17 -0.17453293 2016.08.17.16.27 l u
## 2125 245 6 2016.08.17 -2.00712864 2016.08.17.16.27 l u
## 2126 60 7 2016.08.17 1.04719755 2016.08.17.16.27 l u
## 2127 40 8 2016.08.17 0.69813170 2016.08.17.16.27 l u
## 2128 50 9 2016.08.17 0.87266463 2016.08.17.16.27 l u
## 2129 280 10 2016.08.17 -1.39626340 2016.08.17.16.27 l u
## 2130 40 11 2016.08.17 0.69813170 2016.08.17.16.27 l u
## 2131 10 12 2016.08.17 0.17453293 2016.08.17.16.27 l u
## 2132 260 13 2016.08.17 -1.74532925 2016.08.17.16.27 l u
## 2133 210 14 2016.08.17 -2.61799388 2016.08.17.16.27 l u
## 2134 140 15 2016.08.17 2.44346095 2016.08.17.16.27 l u
## 2135 230 16 2016.08.17 -2.26892803 2016.08.17.16.27 l u
## 2136 70 17 2016.08.17 1.22173048 2016.08.17.16.27 l u
## 2137 210 18 2016.08.17 -2.61799388 2016.08.17.16.27 l u
## 2138 320 19 2016.08.17 -0.69813170 2016.08.17.16.27 h u
## 2139 350 20 2016.08.17 -0.17453293 2016.08.17.16.27 h u
## 2140 345 21 2016.08.17 -0.26179939 2016.08.17.16.27 h u
## 2141 290 22 2016.08.17 -1.22173048 2016.08.17.16.27 h u
## 2142 290 23 2016.08.17 -1.22173048 2016.08.17.16.27 h u
## 2143 330 24 2016.08.17 -0.52359878 2016.08.17.16.27 h u
## 2144 335 25 2016.08.17 -0.43633231 2016.08.17.16.27 h u
## 2145 300 26 2016.08.17 -1.04719755 2016.08.17.16.27 h u
## 2146 300 27 2016.08.17 -1.04719755 2016.08.17.16.27 h u
## 2147 350 28 2016.08.17 -0.17453293 2016.08.17.16.27 h u
## 2148 300 29 2016.08.17 -1.04719755 2016.08.17.16.27 h u
## 2149 305 30 2016.08.17 -0.95993109 2016.08.17.16.27 h u
## 2150 300 31 2016.08.17 -1.04719755 2016.08.17.16.27 h u
## 2151 295 32 2016.08.17 -1.13446401 2016.08.17.16.27 h u
## 2152 280 33 2016.08.17 -1.39626340 2016.08.17.16.27 h u
## 2153 30 1 2016.08.18 0.52359878 2016.08.18.14.01 l u
## 2154 345 2 2016.08.18 -0.26179939 2016.08.18.14.01 l u
## 2155 190 3 2016.08.18 -2.96705973 2016.08.18.14.01 l u
## 2156 180 4 2016.08.18 3.14159265 2016.08.18.14.01 l u
## 2157 240 5 2016.08.18 -2.09439510 2016.08.18.14.01 l u
## 2158 340 6 2016.08.18 -0.34906585 2016.08.18.14.01 l u
## 2159 0 7 2016.08.18 0.00000000 2016.08.18.14.01 l u
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## 2161 10 9 2016.08.18 0.17453293 2016.08.18.14.01 l u
## 2162 280 10 2016.08.18 -1.39626340 2016.08.18.14.01 l u
## 2163 15 11 2016.08.18 0.26179939 2016.08.18.14.01 l u
## 2164 270 12 2016.08.18 -1.57079633 2016.08.18.14.01 l u
## 2165 260 13 2016.08.18 -1.74532925 2016.08.18.14.01 l u
## 2166 330 14 2016.08.18 -0.52359878 2016.08.18.14.01 l u
## 2167 270 15 2016.08.18 -1.57079633 2016.08.18.14.01 l u
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## 2169 340 17 2016.08.18 -0.34906585 2016.08.18.14.01 h u
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## cet_time sun_az sun_az_rad
## 1 2016-05-31 14:24:00 208.3263 -2.647205
## 2 2016-05-31 14:24:00 208.3263 -2.647205
## 3 2016-05-31 14:24:00 208.3263 -2.647205
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## 24 2016-05-31 14:24:00 208.3263 -2.647205
## 25 2016-05-31 14:24:00 208.3263 -2.647205
## 26 2016-05-31 14:24:00 208.3263 -2.647205
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## 84 2016-05-31 14:57:00 221.3982 -2.419059
## 85 2016-05-31 14:57:00 221.3982 -2.419059
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## 89 2016-05-31 15:14:00 227.4222 -2.313920
## 90 2016-05-31 15:14:00 227.4222 -2.313920
## 91 2016-05-31 15:14:00 227.4222 -2.313920
## 92 2016-05-31 15:14:00 227.4222 -2.313920
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## 97 2016-05-31 15:14:00 227.4222 -2.313920
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## 99 2016-05-31 15:14:00 227.4222 -2.313920
## 100 2016-05-31 15:14:00 227.4222 -2.313920
## 101 2016-05-31 15:14:00 227.4222 -2.313920
## 102 2016-05-31 15:14:00 227.4222 -2.313920
## 103 2016-05-31 15:14:00 227.4222 -2.313920
## 104 2016-05-31 14:18:00 205.7573 -2.692044
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## 106 2016-05-31 14:18:00 205.7573 -2.692044
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## 121 2016-05-31 14:18:00 205.7573 -2.692044
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## 129 2016-05-31 14:18:00 205.7573 -2.692044
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## 134 2016-05-31 14:18:00 205.7573 -2.692044
## 135 2016-05-31 14:18:00 205.7573 -2.692044
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## 140 2016-05-31 14:18:00 205.7573 -2.692044
## 141 2016-05-31 14:02:00 198.6482 -2.816120
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## 143 2016-05-31 14:02:00 198.6482 -2.816120
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## 159 2016-05-31 14:02:00 198.6482 -2.816120
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## 161 2016-06-06 14:10:00 202.1606 -2.754817
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## 169 2016-06-06 14:10:00 202.1606 -2.754817
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## 179 2016-06-06 14:10:00 202.1606 -2.754817
## 180 2016-06-06 14:10:00 202.1606 -2.754817
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## 182 2016-06-06 14:10:00 202.1606 -2.754817
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## 198 2016-06-06 14:10:00 202.1606 -2.754817
## 199 2016-06-06 14:10:00 202.1606 -2.754817
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## 201 2016-06-06 14:16:00 204.8475 -2.707921
## 202 2016-06-06 14:16:00 204.8475 -2.707921
## 203 2016-06-06 14:16:00 204.8475 -2.707921
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## 205 2016-06-06 14:16:00 204.8475 -2.707921
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## 207 2016-06-06 14:16:00 204.8475 -2.707921
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## 212 2016-06-06 14:16:00 204.8475 -2.707921
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## 218 2016-06-06 14:16:00 204.8475 -2.707921
## 219 2016-06-06 14:22:00 207.4783 -2.662006
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## 1744 2016-07-12 16:08:00 241.4206 -2.069601
## 1745 2016-07-18 13:31:00 179.9830 3.141296
## 1746 2016-07-18 13:31:00 179.9830 3.141296
## 1747 2016-07-18 13:31:00 179.9830 3.141296
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## 1772 2016-07-18 13:31:00 179.9830 3.141296
## 1773 2016-07-18 13:31:00 179.9830 3.141296
## 1774 2016-07-18 13:31:00 179.9830 3.141296
## 1775 2016-07-18 14:19:00 201.8945 -2.759461
## 1776 2016-07-18 14:19:00 201.8945 -2.759461
## 1777 2016-07-18 14:19:00 201.8945 -2.759461
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## 1799 2016-07-18 14:19:00 201.8945 -2.759461
## 1800 2016-07-18 14:19:00 201.8945 -2.759461
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## 1802 2016-07-18 14:19:00 201.8945 -2.759461
## 1803 2016-07-18 14:19:00 201.8945 -2.759461
## 1804 2016-07-18 14:19:00 201.8945 -2.759461
## 1805 2016-07-18 15:10:00 222.1230 -2.406407
## 1806 2016-07-18 15:10:00 222.1230 -2.406407
## 1807 2016-07-18 15:10:00 222.1230 -2.406407
## 1808 2016-07-18 15:10:00 222.1230 -2.406407
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## 1830 2016-07-18 15:10:00 222.1230 -2.406407
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## 1838 2016-07-18 15:10:00 222.1230 -2.406407
## 1839 2016-07-18 15:10:00 222.1230 -2.406407
## 1840 2016-07-18 15:10:00 222.1230 -2.406407
## 1841 2016-07-18 15:10:00 222.1230 -2.406407
## 1842 2016-07-18 15:10:00 222.1230 -2.406407
## 1843 2016-07-18 15:10:00 222.1230 -2.406407
## 1844 2016-07-18 15:18:00 224.9292 -2.357431
## 1845 2016-07-18 15:18:00 224.9292 -2.357431
## 1846 2016-07-18 15:18:00 224.9292 -2.357431
## 1847 2016-07-18 15:18:00 224.9292 -2.357431
## 1848 2016-07-18 15:18:00 224.9292 -2.357431
## 1849 2016-07-18 15:18:00 224.9292 -2.357431
## 1850 2016-07-18 15:18:00 224.9292 -2.357431
## 1851 2016-07-18 15:18:00 224.9292 -2.357431
## 1852 2016-07-18 15:18:00 224.9292 -2.357431
## 1853 2016-07-18 15:18:00 224.9292 -2.357431
## 1854 2016-07-18 15:18:00 224.9292 -2.357431
## 1855 2016-07-18 15:18:00 224.9292 -2.357431
## 1856 2016-07-18 15:18:00 224.9292 -2.357431
## 1857 2016-07-18 15:18:00 224.9292 -2.357431
## 1858 2016-07-18 15:18:00 224.9292 -2.357431
## 1859 2016-07-18 15:18:00 224.9292 -2.357431
## 1860 2016-07-18 15:18:00 224.9292 -2.357431
## 1861 2016-07-18 15:18:00 224.9292 -2.357431
## 1862 2016-07-18 15:18:00 224.9292 -2.357431
## 1863 2016-07-18 15:18:00 224.9292 -2.357431
## 1864 2016-07-18 15:18:00 224.9292 -2.357431
## 1865 2016-07-18 15:18:00 224.9292 -2.357431
## 1866 2016-07-18 15:18:00 224.9292 -2.357431
## 1867 2016-07-18 15:18:00 224.9292 -2.357431
## 1868 2016-07-18 15:18:00 224.9292 -2.357431
## 1869 2016-07-18 15:18:00 224.9292 -2.357431
## 1870 2016-07-18 15:18:00 224.9292 -2.357431
## 1871 2016-07-18 15:18:00 224.9292 -2.357431
## 1872 2016-07-18 15:18:00 224.9292 -2.357431
## 1873 2016-07-18 15:18:00 224.9292 -2.357431
## 1874 2016-07-18 15:18:00 224.9292 -2.357431
## 1875 2016-07-18 15:18:00 224.9292 -2.357431
## 1876 2016-07-18 15:18:00 224.9292 -2.357431
## 1877 2016-07-18 15:18:00 224.9292 -2.357431
## 1878 2016-07-18 15:18:00 224.9292 -2.357431
## 1879 2016-07-18 15:18:00 224.9292 -2.357431
## 1880 2016-07-18 15:18:00 224.9292 -2.357431
## 1881 2016-07-18 15:18:00 224.9292 -2.357431
## 1882 2016-07-18 15:18:00 224.9292 -2.357431
## 1883 2016-07-18 15:18:00 224.9292 -2.357431
## 1884 2016-07-18 15:18:00 224.9292 -2.357431
## 1885 2016-07-18 15:18:00 224.9292 -2.357431
## 1886 2016-07-18 15:28:00 228.3003 -2.298593
## 1887 2016-07-18 15:28:00 228.3003 -2.298593
## 1888 2016-07-18 15:28:00 228.3003 -2.298593
## 1889 2016-07-18 15:28:00 228.3003 -2.298593
## 1890 2016-07-18 15:28:00 228.3003 -2.298593
## 1891 2016-07-18 15:28:00 228.3003 -2.298593
## 1892 2016-07-18 15:28:00 228.3003 -2.298593
## 1893 2016-07-18 15:28:00 228.3003 -2.298593
## 1894 2016-07-18 15:28:00 228.3003 -2.298593
## 1895 2016-07-18 15:28:00 228.3003 -2.298593
## 1896 2016-07-18 15:28:00 228.3003 -2.298593
## 1897 2016-07-18 15:28:00 228.3003 -2.298593
## 1898 2016-07-18 15:28:00 228.3003 -2.298593
## 1899 2016-07-18 15:28:00 228.3003 -2.298593
## 1900 2016-07-18 15:28:00 228.3003 -2.298593
## 1901 2016-07-18 15:28:00 228.3003 -2.298593
## 1902 2016-07-18 15:28:00 228.3003 -2.298593
## 1903 2016-07-18 15:28:00 228.3003 -2.298593
## 1904 2016-07-18 15:28:00 228.3003 -2.298593
## 1905 2016-07-18 15:28:00 228.3003 -2.298593
## 1906 2016-07-18 15:28:00 228.3003 -2.298593
## 1907 2016-07-18 15:28:00 228.3003 -2.298593
## 1908 2016-07-18 15:28:00 228.3003 -2.298593
## 1909 2016-07-18 15:28:00 228.3003 -2.298593
## 1910 2016-07-18 15:28:00 228.3003 -2.298593
## 1911 2016-07-18 15:28:00 228.3003 -2.298593
## 1912 2016-07-18 15:28:00 228.3003 -2.298593
## 1913 2016-07-18 15:28:00 228.3003 -2.298593
## 1914 2016-07-18 15:28:00 228.3003 -2.298593
## 1915 2016-07-18 15:28:00 228.3003 -2.298593
## 1916 2016-07-18 15:28:00 228.3003 -2.298593
## 1917 2016-07-18 15:28:00 228.3003 -2.298593
## 1918 2016-07-18 15:28:00 228.3003 -2.298593
## 1919 2016-07-19 12:15:00 146.5598 2.557952
## 1920 2016-07-19 12:15:00 146.5598 2.557952
## 1921 2016-07-19 12:15:00 146.5598 2.557952
## 1922 2016-07-19 12:15:00 146.5598 2.557952
## 1923 2016-07-19 12:15:00 146.5598 2.557952
## 1924 2016-07-19 12:15:00 146.5598 2.557952
## 1925 2016-07-19 12:15:00 146.5598 2.557952
## 1926 2016-07-19 12:15:00 146.5598 2.557952
## 1927 2016-07-19 12:15:00 146.5598 2.557952
## 1928 2016-07-19 12:15:00 146.5598 2.557952
## 1929 2016-07-19 12:15:00 146.5598 2.557952
## 1930 2016-07-19 12:15:00 146.5598 2.557952
## 1931 2016-07-19 12:15:00 146.5598 2.557952
## 1932 2016-07-19 12:15:00 146.5598 2.557952
## 1933 2016-07-19 12:15:00 146.5598 2.557952
## 1934 2016-07-19 12:15:00 146.5598 2.557952
## 1935 2016-07-19 12:15:00 146.5598 2.557952
## 1936 2016-07-19 12:15:00 146.5598 2.557952
## 1937 2016-07-19 12:15:00 146.5598 2.557952
## 1938 2016-07-19 12:15:00 146.5598 2.557952
## 1939 2016-07-19 12:15:00 146.5598 2.557952
## 1940 2016-07-19 12:15:00 146.5598 2.557952
## 1941 2016-07-19 12:15:00 146.5598 2.557952
## 1942 2016-07-19 12:15:00 146.5598 2.557952
## 1943 2016-07-19 12:15:00 146.5598 2.557952
## 1944 2016-07-19 12:15:00 146.5598 2.557952
## 1945 2016-07-19 12:15:00 146.5598 2.557952
## 1946 2016-07-19 12:15:00 146.5598 2.557952
## 1947 2016-07-19 12:15:00 146.5598 2.557952
## 1948 2016-07-19 12:15:00 146.5598 2.557952
## 1949 2016-07-19 12:15:00 146.5598 2.557952
## 1950 2016-07-19 12:15:00 146.5598 2.557952
## 1951 2016-07-19 12:15:00 146.5598 2.557952
## 1952 2016-07-19 12:15:00 146.5598 2.557952
## 1953 2016-07-19 12:15:00 146.5598 2.557952
## 1954 2016-07-19 12:15:00 146.5598 2.557952
## 1955 2016-07-19 12:15:00 146.5598 2.557952
## 1956 2016-07-19 12:15:00 146.5598 2.557952
## 1957 2016-07-19 12:15:00 146.5598 2.557952
## 1958 2016-07-19 12:15:00 146.5598 2.557952
## 1959 2016-07-19 12:59:00 165.2010 2.883302
## 1960 2016-07-19 12:59:00 165.2010 2.883302
## 1961 2016-07-19 12:59:00 165.2010 2.883302
## 1962 2016-07-19 12:59:00 165.2010 2.883302
## 1963 2016-07-19 12:59:00 165.2010 2.883302
## 1964 2016-07-19 12:59:00 165.2010 2.883302
## 1965 2016-07-19 12:59:00 165.2010 2.883302
## 1966 2016-07-19 12:59:00 165.2010 2.883302
## 1967 2016-07-19 12:59:00 165.2010 2.883302
## 1968 2016-07-19 12:59:00 165.2010 2.883302
## 1969 2016-07-19 12:59:00 165.2010 2.883302
## 1970 2016-07-19 12:59:00 165.2010 2.883302
## 1971 2016-07-19 12:59:00 165.2010 2.883302
## 1972 2016-07-19 12:59:00 165.2010 2.883302
## 1973 2016-07-19 12:59:00 165.2010 2.883302
## 1974 2016-07-19 12:59:00 165.2010 2.883302
## 1975 2016-07-19 12:59:00 165.2010 2.883302
## 1976 2016-07-19 12:59:00 165.2010 2.883302
## 1977 2016-07-19 12:59:00 165.2010 2.883302
## 1978 2016-07-19 12:59:00 165.2010 2.883302
## 1979 2016-07-19 12:59:00 165.2010 2.883302
## 1980 2016-07-19 12:59:00 165.2010 2.883302
## 1981 2016-07-19 12:59:00 165.2010 2.883302
## 1982 2016-07-19 12:59:00 165.2010 2.883302
## 1983 2016-07-19 12:59:00 165.2010 2.883302
## 1984 2016-07-19 12:59:00 165.2010 2.883302
## 1985 2016-07-19 12:59:00 165.2010 2.883302
## 1986 2016-07-19 12:59:00 165.2010 2.883302
## 1987 2016-07-19 12:59:00 165.2010 2.883302
## 1988 2016-07-19 12:59:00 165.2010 2.883302
## 1989 2016-07-19 12:59:00 165.2010 2.883302
## 1990 2016-07-19 12:59:00 165.2010 2.883302
## 1991 2016-07-19 12:59:00 165.2010 2.883302
## 1992 2016-07-19 12:59:00 165.2010 2.883302
## 1993 2016-07-19 12:59:00 165.2010 2.883302
## 1994 2016-07-19 12:59:00 165.2010 2.883302
## 1995 2016-07-19 13:04:00 167.4652 2.922818
## 1996 2016-07-19 13:04:00 167.4652 2.922818
## 1997 2016-07-19 13:04:00 167.4652 2.922818
## 1998 2016-07-19 13:04:00 167.4652 2.922818
## 1999 2016-07-19 13:04:00 167.4652 2.922818
## 2000 2016-07-19 13:04:00 167.4652 2.922818
## 2001 2016-07-19 13:04:00 167.4652 2.922818
## 2002 2016-07-19 13:04:00 167.4652 2.922818
## 2003 2016-07-19 13:04:00 167.4652 2.922818
## 2004 2016-07-19 13:04:00 167.4652 2.922818
## 2005 2016-07-19 13:04:00 167.4652 2.922818
## 2006 2016-07-19 13:04:00 167.4652 2.922818
## 2007 2016-07-19 13:04:00 167.4652 2.922818
## 2008 2016-07-19 13:04:00 167.4652 2.922818
## 2009 2016-07-19 13:04:00 167.4652 2.922818
## 2010 2016-07-19 13:04:00 167.4652 2.922818
## 2011 2016-07-19 13:04:00 167.4652 2.922818
## 2012 2016-07-19 13:04:00 167.4652 2.922818
## 2013 2016-07-19 13:04:00 167.4652 2.922818
## 2014 2016-07-19 13:04:00 167.4652 2.922818
## 2015 2016-07-19 13:04:00 167.4652 2.922818
## 2016 2016-07-19 13:04:00 167.4652 2.922818
## 2017 2016-07-19 13:04:00 167.4652 2.922818
## 2018 2016-07-19 13:04:00 167.4652 2.922818
## 2019 2016-07-19 13:04:00 167.4652 2.922818
## 2020 2016-07-19 13:04:00 167.4652 2.922818
## 2021 2016-07-19 13:04:00 167.4652 2.922818
## 2022 2016-07-19 13:04:00 167.4652 2.922818
## 2023 2016-07-19 13:04:00 167.4652 2.922818
## 2024 2016-07-19 13:04:00 167.4652 2.922818
## 2025 2016-07-19 13:04:00 167.4652 2.922818
## 2026 2016-07-19 13:04:00 167.4652 2.922818
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## 6224 <NA> NA NA
## 6225 <NA> NA NA
## 6226 <NA> NA NA
## 6227 <NA> NA NA
## 6228 <NA> NA NA
## 6229 <NA> NA NA
## 6230 <NA> NA NA
## 6231 <NA> NA NA## xx intensity nn accuracy wavelength
## 1 -31.208 2.15e+09 13.010 0.14 354
## 2 -20.263 3.69e+09 14.249 0.15 535
## 3 -8.217 6.67e+09 19.135 0.20 354
## 4 -1.342 9.36e+09 15.350 0.16 535
## 5 15.118 2.10e+10 30.769 0.33 354
## 6 24.548 3.35e+10 14.731 0.16 535
## 7 32.671 4.99e+10 70.349 0.74 354
## 8 45.199 9.25e+10 37.928 0.40 535
## 9 42.996 8.30e+10 10.463 0.11 429
## 10 61.994 2.12e+11 75.030 0.79 354
## 11 69.360 3.04e+11 70.349 0.74 535
## 12 71.254 3.34e+11 48.460 0.51 429
## 13 96.412 1.15e+12 85.355 0.90 535
## 14 95.448 1.10e+12 72.208 0.76 429
## 15 104.741 1.74e+12 78.059 0.83 354
## 16 118.026 3.34e+12 80.468 0.85 429
## 17 120.986 3.86e+12 89.657 0.95 535
## 18 141.233 1.05e+13 90.189 0.95 535
## 19 141.352 1.05e+13 83.978 0.89 429
## 20 165.252 3.41e+13 91.722 0.97 535Format data
Ensure that each variable has the correct data format for subsequent analysis.
cd = within(cd,
{
ID = as.factor(ID) # beedance identifier as a factor
date = as.factor(date) # date as a factor
signed_angle = Mod360.180(bearing) # bearing between -180 and 180
angle = circular(rad(signed_angle),# bearing between -pi and pi
rotation = 'clock') # circular format suppresses later warnings
}
)
u_id = with(cd, unique(ID)) # unique beedances
length(u_id)#169 beedances## [1] 169Identify dances in which all four stimulus conditions were used.
luc = sapply(u_id,
FUN = IndCond,
dt = cd)
#Most individuals that made it to bright green
full_ids = u_id[luc == 4]
length(full_ids)#19 individuals## [1] 19Plot the raw dance data
Plot all 169 dances
Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.
Accuracy effects
Calculate the mean vectors for each set of waggle-runs under each lighting condition.
Effect of brightness on mean vector length
Entire dataset
The first thing we notice is that in the low intensity conditions the accuracy is generally lower than for the high intensity conditions.
Within individuals (balanced cases only)
This effect is even clearer if we look at just the full condition dances.
stripchart(mean_vector~colour*brightn,
data = mean_vectors_full,
# add = TRUE,
vertical = TRUE,
method = 'jitter',
jitter = 0.02,
ylim = c(0,1),
col = adjustcolor(c('green2',
'purple',
'darkgreen',
'purple4'), alpha.f = 0.5),
bg = gray(level = 0,
alpha = 0.1),
pch = 21)
#Plot lines linking dances by the same individual
invisible(
{
lapply(X = full_ids,
FUN = Plt_mvec
)
})
abline(h = c(0,1))
Comparison with Edrich et al. (1979)
How does this compare with previous experiments in which a light spot (x°) was presented through bandpass filters and ND filters to produce different intensities? In that data, there was a clear sigmoidal relationship between intensity and accuracy (mean vector length).
Plot raw data from Edrich et al. (1979) Fig. 2
This is best modelled with a nonlinear (psychometric model) following the beta distribution (for variables bounded between zero and one).
Reorganise data
Fit psychometric curves
For each light stimulus, fit a sigmoid curve bounded between baseline
accuracy (shared across stimuli) and maximum accuracy
(1 - lapses). Inflection point and 80%-rise-region width
vary between stimuli, maximising posterior probability for a beta
distribution in (0,1). To do this, we first define a
nonlinear formula in brms.
#set up model fit
formula_beta = bf(
formula = accuracy ~
inv_logit(LogitBase) + (1 - inv_logit(LogitLapse) - inv_logit(LogitBase) ) *#curve region
inv_logit( 4.39*(log10_intensity - Inflex) / exp(LogWidth) ) , #inflection-width curve
# for each of these parameters, we can set up a separate formula
# that describes how to predict them from the data
#Base rate of correct choices: "
LogitBase ~ 1, #Base rate of correct choices: "~ 1" gives the instruction "estimate the mean across all data"
#Lapse rate on a log(odds) scale:
LogitLapse ~ colour, #this is similar to the formula in our LMM example
#inflection point of the initial curve:
Inflex ~ colour, #N.B. this is similar to the intercept, so it does not include effects of stimulus level
#log 80% width of the curve:
LogWidth ~ colour, #N.B. this is similar to the slope, so all of its effects depend on stimulus level
family = Beta(link = "identity", link_phi = 'log'),
nl = TRUE)#the joint distribution for these parameters is undefined, and therefore the parameters themselves are "nonlinear"Since this is a nonlinear model (there are terms both inside and outside the logistic transform) it is important to establish prior distributions for all parameters. These ensure that parameter estimates explore credible ranges during fitting. The baseline is expected to be around \(r = 0.27\), while the maximum accuracy should be around \(r = 0.95\), and their estimates should not converge (that would flatten the curve, or reverse its direction). The inflection points are expected around \(10^{11}\) photons cm\(^{-2}\) s\(^{-1}\), with a rise-region width of \(10^{3}\) photons cm\(^{-2}\) s\(^{-1}\). All colour effects may vary by a few orders of magnitude.
#set up priors
prior_beta = get_prior(formula = formula_beta,
data = ed)
#set the prior distribution
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'LogitBase' &
coef %in% 'Intercept'
] = 'normal(-1,1)' #a normal distribution centred on plogis(-1) = 0.27
})
#this prior is automatically bounded between 0 and 1,
#Lapse rate priors ---------------------------------------------------
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'LogitLapse' &
coef %in% 'Intercept'
] = 'normal(-3,2)' #a normal distribution centred on -3
})
#for all other fixed effects on lapse rate, we'll suggest values around 0 (no effect)
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'LogitLapse' &
coef %in% 'colourblue'
] = 'normal(0,2)' #a normal distribution:mean 0, sd 3
})
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'LogitLapse' &
coef %in% 'colourUV'
] = 'normal(0,2)' #a normal distribution:mean 0, sd 3
})
#Inflection point priors ---------------------------------------------
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'Inflex' &
coef %in% 'Intercept'
] = 'normal(11,2)' #a normal distribution:mean 11, sd 2
})
#for all coefficients, we'll suggest values around 0 (no effect)
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'Inflex' &
coef %in% 'colourblue'
] = 'normal(0,2)' #a normal distribution:mean 0, sd 2
})
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'Inflex' &
coef %in% 'colourUV'
] = 'normal(0,2)' #a normal distribution:mean 0, sd 2
})
#Rise region width priors --------------------------------------------
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'LogWidth' &
coef %in% 'Intercept'
] = 'normal(1,2)' #a normal distribution:mean 1, sd 3
})
#for all coefficients, we'll suggest values around 0 (no effect)
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'LogWidth' &
coef %in% 'colourblue'
] = 'normal(0,2)' #a normal distribution:mean 0, sd 3
})
prior_beta = within(prior_beta,
{ prior[
class %in% 'b' & #just the fixed effects
nlpar %in% 'LogWidth' &
coef %in% 'colourUV'
] = 'normal(0,2)' #a normal distribution:mean 0, sd 3
})Fit a psychometric model to the data using the nonlinear formula and
specified prior distributions. 4000 iterations on
4 chains takes less than one minute.
#takes less than 1 minute
system.time(
{
beta_fit = brm( formula = formula_beta, # using our nonlinear formula
data = ed, # our data
prior = prior_beta, # our priors
iter = 4000, # long run for 4000 iterations
chains = 4, # 4 chains in parallel
cores = 4, # on 4 CPUs
refresh = 0, # don't echo chain progress
control = list(adapt_delta = 0.95), #finer sampling
backend = 'cmdstanr') # use cmdstanr (other compilers broken)
}
)## Start sampling## Running MCMC with 4 parallel chains...
##
## Chain 2 finished in 1.7 seconds.
## Chain 1 finished in 1.8 seconds.
## Chain 3 finished in 2.0 seconds.
## Chain 4 finished in 2.3 seconds.
##
## All 4 chains finished successfully.
## Mean chain execution time: 1.9 seconds.
## Total execution time: 2.6 seconds.## Warning: 1 of 8000 (0.0%) transitions ended with a divergence.
## See https://mc-stan.org/misc/warnings for details.## user system elapsed
## 25.284 1.700 22.504Plot and compare data from Edrich and Kühn.
Summarise the data from full cases in the Kühn data using quantiles (minimum, 25%, median, 75% and maximum).
#Examine quantiles
meanQ = aggregate(mean_vector ~ colour*brightn,
data = mean_vectors_full,
FUN = quantile)
#Extract different quantiles as separate columns in a data frame
meanQ = data.frame(cbind(meanQ[1:2], meanQ$mean_vector) )
#Rename
names(meanQ) = c('colour', 'brightn', paste0('q',0:4))
#Subset by condition
gh_meanQ = subset(meanQ, colour %in% 'g' & brightn %in% 'h')
gl_meanQ = subset(meanQ, colour %in% 'g' & brightn %in% 'l')
uh_meanQ = subset(meanQ, colour %in% 'u' & brightn %in% 'h')
ul_meanQ = subset(meanQ, colour %in% 'u' & brightn %in% 'l')Extract the model predictions by summarising parameter estimates from
the sampling phases of all chains. To identify specific combinations of
parameter values, use the conditional_effects function,
which organises all simultaneous estimates into a data frame.
# #N.B. for plotting we will need to also define "inv_logit" in our the R environment
inv_logit = inv_logit_scaled # this can be found in brms, but with an additional specifier
#summary of parameter estimates
full_sm_beta = summary(beta_fit,
robust = TRUE)#use the median estimate## Warning: There were 1 divergent transitions after warmup. Increasing
## adapt_delta above 0.95 may help. See
## http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup#Extract fixed effects estimates
full_fix_beta = full_sm_beta$fixed
#extract rownames
full_fix_rn_beta = rownames(full_fix_beta)
# stimulus levels to add to the dataset to be able to measure this effect.
full_estimates_beta = full_fix_beta$Estimate
names(full_estimates_beta) = full_fix_rn_beta
# to predict all effects, we can use the 'posterior_epred' method
#by default 100 predictions per continuous variable (but fewer for their interactions)
#This takes <2 seconds
system.time(
{
full_cond_beta =brms::conditional_effects(beta_fit,
method = 'posterior_epred', # posterior epred not working
cores = parallel::detectCores()-1,
effects = c('log10_intensity:colour'),
plot = FALSE
)
}
)## user system elapsed
## 1.881 0.174 2.056#extract predictions
pred_data_beta = full_cond_beta$`log10_intensity:colour`
#Green light curve
g_curve =
with(data.frame(t(full_estimates_beta)),
{
list(Base = plogis(LogitBase_Intercept),
Maxima = 1- plogis(LogitLapse_Intercept),
Inflection = Inflex_Intercept,
Width = exp(LogWidth_Intercept)
)
}
)
#UV light curve
u_curve =
with(data.frame(t(full_estimates_beta)),
{
list(Base = plogis(LogitBase_Intercept),
Maxima = 1- plogis(LogitLapse_Intercept + LogitLapse_colourUV),
Inflection = Inflex_Intercept + Inflex_colourUV,
Width = exp(LogWidth_Intercept + LogWidth_colourUV)
)
}
)Plot the raw data alongside the predictions for the data from Edrich et al., (1979) and a boxplot summary of the data data from Kühn (2017).
#Prepare a sequence for plotting
xxl = seq(from = 9, to = 16,
length.out = 1e3)
#plot only the stimulus types also used by Kühn.
ed_ug = subset(ed, wavelength != 429)
#plot each stimulus type
with(ed_ug,
{
plot(x = log10_intensity,
y = accuracy,
main =
'Comparison of data from Edrich et al. 1979
with Kühn, 2017',
xlab = 'log10(intensity) (photons/cm2/s)',
ylab = 'accuracy (r)',
ylim = c(0,1),
xlim = c(9,16),
pch = 21,
cex = 1.5,
col = 'black',
bg = sapply(paste(wavelength),
FUN = switch,
`354` = 'purple',
`429` = 'blue',
`535` = 'darkgreen',
'red')
)
abline(h = c(0,1))
abline(v = log10(4*c(1e12,1e14)) )
}
)
#Add the estimated range of the curve for the green stimulus
with(data.frame(t(full_estimates_beta)),
{
abline(h = c(0,1,
plogis(LogitBase_Intercept),
1- plogis(LogitLapse_Intercept) ),
lty = c(1,1,3,3)
)
}
)
#plot total 95% prediction intervals
with(subset(pred_data_beta, colour == '0green'),
{
polygon(x = c(sort(log10_intensity), rev(sort(log10_intensity))),
y = c(lower__[order(log10_intensity)],
rev(upper__[order(log10_intensity)])
),
col = adjustcolor('green', alpha.f = 25/256),
border = NA,
lwd = 0.1
)
}
)
with(subset(pred_data_beta, colour == 'UV'),
{
polygon(x = c(sort(log10_intensity), rev(sort(log10_intensity))),
y = c(lower__[order(log10_intensity)],
rev(upper__[order(log10_intensity)])
),
col = adjustcolor('magenta', alpha.f = 25/256),
border = NA,
lwd = 0.1
)
}
)
#plot the median prediction lines
with(g_curve,
lines(x = xxl,
y = Base + (Maxima - Base) *
plogis(4.39*(xxl - Inflection)/Width),
col = 'darkgreen',
lwd = 3,
lty = 3)
)
with(u_curve,
lines(x = xxl,
y = Base + (Maxima - Base) *
plogis(4.39*(xxl - Inflection)/Width),
col = 'purple4',
lwd = 3,
lty = 3)
)
#plot observed data from Kühn as boxplots showing the quartiles, median and total range.
#Green High intensity
QBox(quant = subset(meanQ, colour %in% 'g' & brightn %in% 'h'),
x = log10(4e14),
offset = -0.1,
cols = c('green', 'darkgreen')
)
#Green Low intensity
QBox(quant = subset(meanQ, colour %in% 'g' & brightn %in% 'l'),
x = log10(4e12),
offset = -0.1,
cols = c('green', 'darkgreen')
)
#UV High intensity
QBox(quant = subset(meanQ, colour %in% 'u' & brightn %in% 'h'),
x = log10(4e14),
offset = 0.1,
cols = c('magenta', 'purple')
)
#UV Low intensity
QBox(quant = subset(meanQ, colour %in% 'u' & brightn %in% 'l'),
x = log10(4e12),
offset = 0.1,
cols = c('magenta', 'purple')
)
legend(x = 'bottomright',
legend = c(
paste('Edrich',
sort(unique(ed_ug$wavelength),
decreasing = TRUE), 'nm'),
paste(' Kühn', c(528, 365), 'nm' )
),
col = c('darkgreen', 'purple', 'green', 'magenta'),
pch = c(20, 20, 15, 15),
lty = c(3,3,NA, NA),
lwd = 3,
cex = 0.7)
It would be difficult to explain the orientation accuracy for the high intensity (\(4*10^{14}\)) UV stimulus from the accuracy curve for Edrich’s UV data, but it would fit well with the maximum accuracy observed for green light. In Edrich’s study, the green light was interpreted as the sun (dances at correct angle between sun and feeder), whereas the UV light was interpreted as a patch of sky near the anti-sun. In Kühn’s data the stimuli were smaller (assuming a viewing distance of ≈200mm, an SMD with diameter 3.5mm would appear \(deg(2*atan2(y = 3.5/2,x = 200)) =\) 1.0° across) than Edrich’s (2.3°), which may have resulted in them being perceived as dimmer (left shift in this graph).
Sun compass orientation
Since most dances were at least somewhat oriented (\(r>0.5\)) we can assume that the mean angles of these dances typically align with an intended dance direction. If most dances are for the same geographic location, we should observe dances as the same fixed angle to the stimulus, interpreted either as the sun or the anti-sun.
sun_diff_gh = sapply(X = u_id,
FUN = SunDiff,
dt = mean_vectors,
cl = 'g',
br = 'h')
sun_diff_gl = sapply(X = u_id,
FUN = SunDiff,
dt = mean_vectors,
cl = 'g',
br = 'l')
sun_diff_uh = sapply(X = u_id,
FUN = SunDiff,
dt = mean_vectors,
cl = 'u',
br = 'h')
sun_diff_ul = sapply(X = u_id,
FUN = SunDiff,
dt = mean_vectors,
cl = 'u',
br = 'l')
par(mfrow = c(2,2), mar = c(0,0,0,0))
PCfun(angles = unlist(sun_diff_gh),
col = 'green',
shrink = 2.0,
side = 3,
title = 'Green Bright')
PCfun(angles = unlist(sun_diff_gl),
col = 'darkgreen',
shrink = 2.0,
side = 3,
title = 'Green Dim')
PCfun(angles = unlist(sun_diff_uh),
col = 'magenta',
shrink = 2.0,
side = 3,
title = 'UV Bright')
PCfun(angles = unlist(sun_diff_ul),
col = 'purple',
shrink = 2.0,
side = 3,
title = ' UV Dim')
For the bright stimuli the dances generally indicate South, but with a very wide range. (or possibly clusters to the South-West and South-East). For the dim stimuli there is less of a clear pattern, particularly for UV dim.
We can also restrict this analysis to just the dances with all conditions.
full_sun_diff_gh = sapply(X = full_ids,
FUN = SunDiff,
dt = mean_vectors,
cl = 'g',
br = 'h')
full_sun_diff_gl = sapply(X = full_ids,
FUN = SunDiff,
dt = mean_vectors,
cl = 'g',
br = 'l')
full_sun_diff_uh = sapply(X = full_ids,
FUN = SunDiff,
dt = mean_vectors,
cl = 'u',
br = 'h')
full_sun_diff_ul = sapply(X = full_ids,
FUN = SunDiff,
dt = mean_vectors,
cl = 'u',
br = 'l')
par(mfrow = c(2,2), mar = c(0,0,0,0))
PCfun(angles = unlist(full_sun_diff_gh),
col = 'green',
shrink = 1.5,
side = 3,
title = 'Green Bright')
PCfun(angles = unlist(full_sun_diff_gl),
col = 'darkgreen',
shrink = 1.5,
side = 3,
title = 'Green Dim')
PCfun(angles = unlist(full_sun_diff_uh),
col = 'magenta',
shrink = 1.5,
side = 3,
title = 'UV Bright')
PCfun(angles = unlist(full_sun_diff_ul),
col = 'purple',
shrink = 1.5,
side = 3,
title = 'UV Dim')
When restricting to only the balanced cases, the pattern becomes clearer. For the most oriented dances to the bright UV stimulus there are two clusters to the South-West and South-East. These are likely also present for the bright green stimulus. The dim green stimulus appears to align somewhat with the bright stimuli. The dim UV stimulus shows no apparent patten, though a slight southwards bias.
Inspect dance angles relative to the stimulus
Mean dance angles relative to the stimulus
Since dances do not point to a specific geographic location, it is possible that they advertise a variety of directions relative to the sun, or are not menotactic but phototactic or uniformly oriented. We can identify phototactic orientation from the angle relative to the stimulus.
par(mfrow = c(2,2), mar = c(0,0,0,0))
PCfun(angles = subset(mean_vectors_full,
subset = colour %in% 'g' & brightn %in% 'h')$mu,
col = 'green',
shrink = 1.5,
title = 'Green Bright')
PCfun(angles = subset(mean_vectors_full,
subset = colour %in% 'g' & brightn %in% 'l')$mu,
col = 'darkgreen',
shrink = 1.5,
title = 'Green Dim')
PCfun(angles = subset(mean_vectors_full,
subset = colour %in% 'u' & brightn %in% 'h')$mu,
col = 'magenta',
shrink = 1.5,
title = 'UV Bright')
PCfun(angles = subset(mean_vectors_full,
subset = colour %in% 'u' & brightn %in% 'l')$mu,
col = 'purple',
shrink = 1.5,
title = 'UV Dim')
While there are some dances towards or near to the stimulus for most conditions, there is a wide spread, suggesting a factor other than phototaxis sets dance directions. N.B. for the dim stimuli where the widest spread is observed, the dances are also less accurate, which may increase variation in mean dance angle.
Change in mean dance angle between stimuli
Change arcs
To determine whether these dances interpret the stimuli as the sun, anti-sun or something else, we would need to check the differences in dance angle between the conditions. It is also worth considering any differences in accuracy between dances to each condition, since this would influence the variation in angular change. These can be visualised as arcs.
#TODO make a function for this
par(mfrow = c(2,2), mar = c(0,0,0,0))
OpenCplot(n_sample = with(full_cd, median(run)/4) )
mtext(text = 'Green Bright to Green Dim',
side = 1,
line = -1,
cex = 0.5)
#open the loop
for(ii in mean_vectors_full$ID)
{
with(subset(mean_vectors_full,
subset = ID %in% ii),
{
DiffArc(a1 = mu[colour %in% 'g' &
brightn %in% 'h'],
a2 = mu[colour %in% 'g' &
brightn %in% 'l'],
r1 = mean_vector[colour %in% 'g' &
brightn %in% 'h'],
r2 = mean_vector[colour %in% 'g' &
brightn %in% 'l'],
col1 = 'green',
col2 = 'darkgreen'
)
}
)
}
OpenCplot(n_sample = with(full_cd, median(run)/4) )
mtext(text = 'UV Bright to UV Dim',
side = 1,
line = -1,
cex = 0.5)
for(ii in mean_vectors_full$ID)
{
with(subset(mean_vectors_full,
subset = ID %in% ii),
{
DiffArc(a1 = mu[colour %in% 'u' &
brightn %in% 'h'],
a2 = mu[colour %in% 'u' &
brightn %in% 'l'],
r1 = mean_vector[colour %in% 'u' &
brightn %in% 'h'],
r2 = mean_vector[colour %in% 'u' &
brightn %in% 'l'],
col1 = 'magenta',
col2 = 'purple'
)
}
)
}
OpenCplot(n_sample = with(full_cd, median(run)/4) )
mtext(text = 'Green Bright to UV Bright',
side = 1,
line = -1,
cex = 0.5)
for(ii in mean_vectors_full$ID)
{
with(subset(mean_vectors_full,
subset = ID %in% ii),
{
DiffArc(a1 = mu[colour %in% 'g' &
brightn %in% 'h'],
a2 = mu[colour %in% 'u' &
brightn %in% 'h'],
r1 = mean_vector[colour %in% 'g' &
brightn %in% 'h'],
r2 = mean_vector[colour %in% 'u' &
brightn %in% 'h'],
col1 = 'green',
col2 = 'magenta'
)
}
)
}
OpenCplot(n_sample = with(full_cd, median(run)/4) )
for(ii in mean_vectors_full$ID)
{
with(subset(mean_vectors_full,
subset = ID %in% ii),
{
DiffArc(a1 = mu[colour %in% 'g' &
brightn %in% 'l'],
a2 = mu[colour %in% 'u' &
brightn %in% 'l'],
r1 = mean_vector[colour %in% 'g' &
brightn %in% 'l'],
r2 = mean_vector[colour %in% 'u' &
brightn %in% 'l'],
col1 = 'darkgreen',
col2 = 'purple'
)
}
)
}
mtext(text = 'Green Dim to UV Dim',
side = 1,
line = -1,
cex = 0.5)
Differences in mean angle
mu_diff_gl = sapply(X = full_ids,
FUN = MuDiff,
dt = mean_vectors_full,
cl = 'g',
br = 'l')
mu_diff_uh = sapply(X = full_ids,
FUN = MuDiff,
dt = mean_vectors_full,
cl = 'u',
br = 'h')
mu_diff_ul = sapply(X = full_ids,
FUN = MuDiff,
dt = mean_vectors_full,
cl = 'u',
br = 'l')
#Other contrasts
mu_diff_uhl = sapply(X = full_ids,
FUN = MuDiff,
dt = mean_vectors_full,
cl = 'u',
br = 'l',
ref_cl = 'u',
ref_br = 'h')
mu_diff_gul = sapply(X = full_ids,
FUN = MuDiff,
dt = mean_vectors_full,
cl = 'u',
br = 'l',
ref_cl = 'g',
ref_br = 'h')
par(mfrow = c(2,2), mar = c(0,0,0,0))
PCfun(angles = unlist(mu_diff_gl),
col = 'darkgreen',
shrink = 1.5,
title = 'Green Dim - Green Bright')
PCfun(angles = unlist(mu_diff_uhl),
col = 'purple',
shrink = 1.5,
title = 'UV Dim - UV Bright')
PCfun(angles = unlist(mu_diff_uh),
col = 'gray40',
shrink = 1.5,
title = 'UV Bright - Green Bright')
PCfun(angles = unlist(mu_diff_gul),
col = 'gray25',
shrink = 1.5,
title = 'UV Dim - Green Dim')
Estimate turn effects
Find fit maximum likelihood turn distributions
For each change distribution, find the maximum likelihood von Mises distribution. For the UV high to UV low change, this will be a bimodal distribution.
#collect all heading differences
pair_diffs_lst = lapply(X = list(mu_diff_gl,
mu_diff_uh,
mu_diff_ul,
mu_diff_gul),
FUN = unlist)
#Give a simpler name
names(pair_diffs_lst) = c('green_hl',
'uvg_h',
'uvg_hl',
'uvg_l')
#Provide appropriate data format
angle_unit = 'degrees'
angle_rot = 'clock'
#make sure they are in circular format
pair_diffs_lst = lapply(X = pair_diffs_lst,
FUN = circular,
units = angle_unit,
rotation = angle_rot)Fit the maximum likelihood distribution for no difference between pairs, differences between pairs, and differences between pairs with two means. If angles shift in one direction between trials, the “difference” distribution should have significantly higher likelihood. If angles shift in two directions between pairs, then the “two means” distribution should be the best fit.
#TODO neaten up!
#Distribution for same means
ml_same_lst = lapply(X = pair_diffs_lst,
mle.vonmises,
bias = TRUE,
mu = circular(x = 0,
units = angle_unit,
rotation = angle_rot)
)
#Distribution for different means
ml_diff_lst = lapply(X = pair_diffs_lst,
mle.vonmises,
bias = TRUE)
#Distribution for multiple different means
mod_diff_lst = lapply(X = pair_diffs_lst,
FUN = circ_mle,#converts circular format data to radians
niter = 1e4)#some stochastic variability for green stim## Warning in check_data(data): Converting from degrees to radians...## Warning in check_data(data): Converting to modulo 2pi...## Warning in check_data(data): Converting from degrees to radians...## Warning in check_data(data): Converting to modulo 2pi...## Warning in check_data(data): Converting from degrees to radians...## Warning in check_data(data): Converting to modulo 2pi...## Warning in check_data(data): Converting from degrees to radians...## Warning in check_data(data): Converting to modulo 2pi...#Forced multiple different means
bim_diff_lst = lapply(X = pair_diffs_lst,
FUN = circ_mle,#converts circular format data to radians
exclude = c('M1','M2A', 'M2B', 'M2C'),#no uniform or unimodal
niter = 1e4)#some stochastic variability for green stim## Warning in check_data(data): Converting from degrees to radians...
## Warning in check_data(data): Converting to modulo 2pi...## Warning in check_data(data): Converting from degrees to radians...## Warning in check_data(data): Converting to modulo 2pi...## Warning in check_data(data): Converting from degrees to radians...## Warning in check_data(data): Converting to modulo 2pi...## Warning in check_data(data): Converting from degrees to radians...## Warning in check_data(data): Converting to modulo 2pi...#Extract the parameters of the model with the lowest AIC
mod_diff_par = t( sapply(X = mod_diff_lst,
FUN = MD_extract) )
bim_diff_par = t( sapply(X = bim_diff_lst,
FUN = MD_extract) )
# Calculate likelihood
#calculate all in list
all_ll = mapply(FUN = LLcalc,
ml = c(ml_same_lst, ml_diff_lst), #apply to both sets of ML estimates
angles = pair_diffs_lst, #repeat datasets
au = angle_unit, #important, use the same frame of reference as the original
ar = angle_rot)
#inspect resulting parameters
mod_diff_results = do.call(rbind, c(ml_same_lst, ml_diff_lst))
#add easy to parse names
rownames(mod_diff_results) = paste( sort( #distinguish same and different mean
rep(x = c( 'same', 'diff'),
times = length(pair_diffs_lst) ),
decreasing = TRUE
),
rep(x = names(pair_diffs_lst),
times = 2)
)
#display version
rspar = mod_diff_results[,c('mu', 'kappa', 'se.mu', 'se.kappa')]
rspar = cbind(rspar, loglikelihood = all_ll)
rspar = apply(X = rspar, MARGIN = 2, FUN = unlist)
#reorder for easy comparison
rspar = rspar[c(rbind(1:4, 1:4+4)),]#put the different directly after the same
rspar[,3:4] = NA
rspar = cbind(rspar, weight1 = 1.0)
colnames(rspar) = colnames(bim_diff_par)[c(1:4, 6:5)]
all_res = rbind(data.frame(rspar),
data.frame(bim_diff_par) )
all_res = apply(all_res, MARGIN = 2, FUN = unlist)
rownames(all_res[9:12,]) = paste('multi', rownames(bim_diff_par))
all_res = all_res[c(1:2, 9, 3:4, 10, 5:6, 11, 7:8, 12),]
all_res = within(data = data.frame(all_res),
{
model = c('same',
'diff',
'multi')
dataset = c(sapply(X = names(pair_diffs_lst),
FUN = rep,
times = 3) )
}
)
# print(rspar, digits = 3)
# print(mod_diff_par, digits = 3)
# print(bim_diff_par, digits = 3)
print(all_res, digits = 3)## mu1 kappa1 mu2 kappa2 loglikelihood weight1 dataset model
## same green_hl 0.0000 2.046 NA NA -19.3 1.000 green_hl same
## diff green_hl 17.4565 2.361 NA NA -17.7 1.000 green_hl diff
## green_hl 350.8794 18.393 56.7 5.82 -14.3 0.569 green_hl multi
## same uvg_h 0.0000 4.464 NA NA -10.9 1.000 uvg_h same
## diff uvg_h -13.1081 5.827 NA NA -8.4 1.000 uvg_h diff
## uvg_h 0.0573 3.836 311.5 4.23 -11.4 0.747 uvg_h multi
## same uvg_hl 0.0000 0.184 NA NA -30.7 1.000 uvg_hl same
## diff uvg_hl 58.3920 0.786 NA NA -28.2 1.000 uvg_hl diff
## uvg_hl 312.7204 4.979 89.3 4.98 -22.1 0.347 uvg_hl multi
## same uvg_l 0.0000 0.184 NA NA -30.7 1.000 uvg_l same
## diff uvg_l 58.3920 0.786 NA NA -28.2 1.000 uvg_l diff
## uvg_l 312.7204 4.979 89.3 4.98 -22.1 0.347 uvg_l multiAs expected, the bimodal models fitted by circ_mle have
the highest likelihood, followed by the models for differences and then
the models for no difference. The difference models require at ≥1 more
parameter, so should increase likelihood by >1 order of magnitude to
be appropriate. The bimodal model require ≥2 more parameters, so should
increase likelihood by >2 log units.
Estimate confidence intervals
For each mean, simulate a distribution of mean estimates
#estimate CI for unimodal von Mises models
mle_CI = with(data.frame(mod_diff_results),
{
mapply(FUN = CI_vM,
angles = pair_diffs_lst,
m1 = mu,
k1 = kappa,
w1 = 1,
alternative = 'two.sided',#not a hypothesis test (symmetrical)
n = 1e4)#takes ≈30s for 10 000 simulations
}
)
#reorder for comparison like the original models
mle_CI = t(mle_CI)[c(rbind(1:4, 1:4+4)),]
rownames(mle_CI) = rownames(rspar)
colnames(mle_CI) = c('lower','median','upper')
#estimate CI for unimodal and bimodal von Mises models
mod_CI = with(data.frame(mod_diff_par),
{
mapply(FUN = CI_vM,
angles = pair_diffs_lst,
m1 = mu1,
k1 = kappa1,
m2 = mu2,
k2 = kappa2,
w1 = weight1,
alternative = 'two.sided',#not a hypothesis test (symmetrical)
# SIMPLIFY = FALSE,
n = 1e4)#takes ≈15 for 10 000 simulations
}
)
#estimate CI for unimodal and bimodal von Mises models
bim_CI = with(data.frame(bim_diff_par),
{
mapply(FUN = CI_vM,
angles = pair_diffs_lst,
m1 = mu1,
k1 = kappa1,
m2 = mu2,
k2 = kappa2,
w1 = weight1,
SIMPLIFY = FALSE,
alternative = 'two.sided',#not a hypothesis test (symmetrical)
n = 1e4)#takes ≈15 for 10 000 simulations
}
)
#collapse to printable table
mod_CI_tb = Table_vCI(mod_CI)
bim_CI_tb = Table_vCI(bim_CI)
print(mle_CI, digits = 3)## lower median upper
## same green_hl 22.72 -0.2377 -23.178
## diff green_hl 38.95 17.5460 -3.594
## same uvg_h 13.51 -0.0435 -13.592
## diff uvg_h -1.05 -13.0742 -24.900
## same uvg_hl 160.47 0.0897 -159.104
## diff uvg_hl 116.88 58.2862 0.837
## same uvg_l 160.65 -0.6450 -159.404
## diff uvg_l 116.09 58.1192 0.729## m1.lower m1.median m1.upper m2.lower m2.median m2.upper
## green_hl 35.64 17.6 -0.969 NA NA NA
## uvg_h -2.32 -13.1 -23.862 NA NA NA
## uvg_hl -24.94 -47.1 -69.241 105 89.4 73.1
## uvg_l -25.64 -47.3 -69.346 106 89.3 73.2We see here that while the confidence interval for the difference distribution between the two green conditions and the two bright conditions nearly overlap with 0° (and the 0° distribution CI overlap with the mean difference), for differences between green lights and dim UV there is a bimodal distribution with CI that to not overlap with 0°. N.B. For one-sided calculations, the CI do overlap with 0° for green conditions, bright conditions and the leftmost mean for dim conditions. ### Plot difference CI
#TODO make bimodal version of PCfun
par(mfrow = c(2,2), mar = c(0,0,0,0))
PCfun(angles = unlist(mu_diff_gl),
col = 'darkgreen',
shrink = 1.5,
title = 'Green Dim - Green Bright')
# PlotCI_vM(mod_CI_tb['green_hl',],
# col = 'darkgreen',
# radius = 1+0.3)
PlotCI_vM(mle_CI['diff green_hl',],
col = 'darkgreen',
radius = 1+0.3)
plot.circular(x = circular(unlist(mu_diff_ul),
units = angle_unit,
rot = angle_rot
),
col = 'purple',
stack = TRUE,
sep = 0.1,
bins = 355/5,
units = angle_unit,
rotation = angle_rot,
zero = pi/2,
shrink = 1.5)
mtext(text = 'UV Dim - Green Bright',
side = 1,
line = -2)
lines(x = c(0,0),
y = c(-1,1),
col = 'gray')
PlotMV_circMLE(mod_par = mod_diff_par['uvg_hl',],
col1 = 'purple')
PlotCI_vM(mod_CI_tb['uvg_hl',],
col = 'purple',
radius = 1+0.3)
PCfun(angles = unlist(mu_diff_uh),
col = 'gray40',
shrink = 1.5,
title = 'UV Bright - Green Bright')
PlotCI_vM(mod_CI_tb['uvg_h',],
col = 'gray40',
radius = 1+0.3)
#according to model comparison, this is slightly better
#But this is not truly bimodal, kappa2 = 0
# plot.circular(x = circular(unlist(mu_diff_uh),
# units = angle_unit,
# rot = angle_rot
# ),
# col = 'gray40',
# stack = TRUE,
# sep = 0.1,
# bins = 355/5,
# units = angle_unit,
# rotation = angle_rot,
# zero = pi/2,
# shrink = 1.5)
# mtext(text = 'UV Bright - Green Bright',
# side = 1,
# line = -2)
# lines(x = c(0,0),
# y = c(-1,1),
# col = 'gray')
# PlotMV_circMLE(mod_par = bim_diff_par['uvg_h',],
# col1 = 'gray40')
# PlotCI_vM(bim_CI_tb['uvg_h',],
# col = 'gray40',
# radius = 1+0.3)
plot.circular(x = circular(unlist(mu_diff_gul),
units = angle_unit,
rot = angle_rot
),
col = 'gray25',
stack = TRUE,
sep = 0.1,
bins = 355/5,
units = angle_unit,
rotation = angle_rot,
zero = pi/2,
shrink = 1.5)
mtext(text = 'UV Dim - Green Dim',
side = 1,
line = -2)
lines(x = c(0,0),
y = c(-1,1),
col = 'gray')
PlotMV_circMLE(mod_par = mod_diff_par['uvg_l',],
col1 = 'gray25')
PlotCI_vM(mod_CI_tb['uvg_l',],
col = 'gray25',
radius = 1+0.3)
Here we see that the confidence interval for the difference between the
green conditions overlaps with 0°, and the one for the two bright
conditions almost does (the one sided CI does, but looks odd due it its
asymmetry). To confirm whether these models better explain the data than
the null hypothesis of the same mean for each condition (no difference),
we can perform a likelihood-ratio test.
Likelihood ratio tests
For each condition, compare the models for same mean, different mean and multiple means. First perform all tests separately, then collect them together and finally adjust for multiple tests before reporting.
mod_details= lapply(X = names(pair_diffs_lst),
FUN = CollectDetails,
ll = all_res,
bimod = TRUE)
names(mod_details) = names(pair_diffs_lst)
#set up tests for hypotheses
lr_tests = c('pairs_diff_zero', #is the turn different from zero?
'pairs_multi_diff', #is the turn in one or two directions?
'pairs_multi_zero' #are the two directions different from zero?
)#multiple tests
#Perform collect likelihood ratio tests for each hypothesis
all_lr_results_lst = lapply(X =mod_details,
FUN = LR_calc_lst,
tst = lr_tests)
all_lr_results = do.call(what = rbind,
args = all_lr_results_lst
)
all_lr_results = within(data.frame(all_lr_results),
{
comparison = c( sapply(X = names(mod_details),
FUN = rep,
times = length(lr_tests)
) )
test = rep(lr_tests,
times = length(names(mod_details))
)
}
)
# lapply(
# all_lr_results_lst,
# FUN = print,
# digits = 3
# )
#add labels to interpret each test according to p value and sign of comparison
all_lr_results = within(all_lr_results,
{
result = mapply(tst = lr_tests,
d0 = unlist(dev0),
d1 = unlist(dev1),
pa = p_adjusted,
FUN = H1label
)
}
)
num_col = sapply(X = all_lr_results, FUN = is.numeric)
print_lr_results = all_lr_results
print_lr_results[,num_col] = apply(print_lr_results[,num_col], MARGIN = 2, FUN = round, digits = 3)
print_lr_results = within(print_lr_results,
{
rm(dev0,dev1, p)
test = sub(sub(sub(test,
pattern = '_',
replacement = ' '),
pattern = '_',
replacement = ' '),
pattern = 'pairs ',
replacement = '')
}
)
rownames(print_lr_results) = with(print_lr_results, paste(comparison, test))#better to keep them for the html
print(print_lr_results,
digits = 3)## d.f. chi_squared p_adjusted test comparison
## green_hl diff zero 1 3.312 0.081 diff zero green_hl
## green_hl multi diff 3 6.723 0.081 multi diff green_hl
## green_hl multi zero 4 10.035 0.081 multi zero green_hl
## uvg_h diff zero 1 5.044 0.074 diff zero uvg_h
## uvg_h multi diff 3 5.929 0.173 multi diff uvg_h
## uvg_h multi zero 4 0.886 0.927 multi zero uvg_h
## uvg_hl diff zero 1 4.983 0.026 diff zero uvg_hl
## uvg_hl multi diff 3 12.274 0.010 multi diff uvg_hl
## uvg_hl multi zero 4 17.257 0.005 multi zero uvg_hl
## uvg_l diff zero 1 4.983 0.026 diff zero uvg_l
## uvg_l multi diff 3 12.274 0.010 multi diff uvg_l
## uvg_l multi zero 4 17.257 0.005 multi zero uvg_l
## result
## green_hl diff zero paired trials _do not_ differ significantly
## green_hl multi diff paired trials _do not_ differ significantly with no single mean
## green_hl multi zero paired trials _do not_ differ significantly with multiple means
## uvg_h diff zero paired trials _do not_ differ significantly
## uvg_h multi diff paired trials _do not_ differ significantly with no single mean
## uvg_h multi zero paired trials _do not_ differ significantly with multiple means
## uvg_hl diff zero paired trials differ significantly
## uvg_hl multi diff paired trials differ significantly with no single mean
## uvg_hl multi zero paired trials differ significantly with multiple means
## uvg_l diff zero paired trials differ significantly
## uvg_l multi diff paired trials differ significantly with no single mean
## uvg_l multi zero paired trials differ significantly with multiple meansThese tests confirm, that there is no significant difference between the two green conditions, a significant 13° left turn between the bright conditions, and significant bimodal differences between the two UV conditions and the two dim conditions, driven by left and right turns for the dim UV condition.